Topology of surfaces, knots, and manifolds

a first undergraduate course by Stephan C Carlson

Publisher: J. Wiley in New York

Written in English
Cover of: Topology of surfaces, knots, and manifolds | Stephan C Carlson
Published: Pages: 157 Downloads: 275
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Subjects:

  • Topology

Edition Notes

Includes bibliographical references (p. 151-153) and index

StatementStephan C. Carlson
Classifications
LC ClassificationsQA611 .C328 2001
The Physical Object
Paginationxii, 157 p. :
Number of Pages157
ID Numbers
Open LibraryOL17000012M
ISBN 100471355445
LC Control Number00063294

( views) Four-manifolds, Geometries and Knots by Jonathan Hillman - arXiv, The goal of the book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such knots. A surface is simply a 2-manifold. The classification theorem for compact connected surfaces (with boundary) is commonly regarded in the categories TOP, DIFF and known proofs (e.g. via triangulations, or Morse theory) yield the same classification because of results that connect these categories for surfaces. Informally speaking, here is what I know to be true for compact . This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in . Topology - Topology - Algebraic topology: The idea of associating algebraic objects or structures with topological spaces arose early in the history of topology. The basic incentive in this regard was to find topological invariants associated with different structures. The simplest example is the Euler characteristic, which is a number associated with a surface.

loop theorem and the sphere theorem. The study of surfaces in 3-manifolds would advance immeasurably. The Georgia Topology Institute was preceded by an 8-week Topology Institute for Graduate Students, mostly from the southern United States. Lecture duties were shared between Bing and Deane Montgomery. Required book: Topology of Surfaces, Knots, and Manifolds by Stefan Carlson. I will follow Carlson’s text, sometimes detouring to treat a topic in more depth/rigor. Other course materials: My (handwritten) lecture notes will be posted on online. Occasionally, there may be typed supplemental notes or xeroxed readings.   In the 's H. Siefert showed that any knot can be viewed as the boundary of an orientable surface with boundary, and gave a relatively simple procedure fo. This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.

$\begingroup$ Hatcher's book is very well-written with a good combination of motivation, intuitive explanations, and rigorous details. It would be worth a decent price, so it is very generous of Dr. Hatcher to provide the book for free download. But if you want an alternative, Greenberg and Harper's Algebraic Topology covers the theory in a straightforward and comprehensive manner. This book, written for the mathematician, does not follow the physical line of reasoning that has been employed to obtain invariants of knots and 3-manifolds. Instead, it endeavors to remain as rigorous as possible, and thus the approaches using conformal field theory or Chern-Simons field theory are not developed by the author (this is not to. A polygonal knot is a knot whose image in R 3 is the union of a finite set of line segments. A tame knot is any knot equivalent to a polygonal knot. Knots which are not tame are called wild, and can have pathological behavior. In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame. Framed knot. A framed knot is the . An Introduction to Geometric Topology [pdf] () points by espeed on mathgenius on From the preface: """ this book is an introduction to surfaces and three-manifolds, and to their geometrisation, due to Poincaré and Koebe in in dimension two and to Thurston and Perelmann in in dimension three.

Topology of surfaces, knots, and manifolds by Stephan C Carlson Download PDF EPUB FB2

This book presents the topology of surfaces, manifolds and knots in a manner that is reachable for undergraduate students with only a knowledge of calculus. Some linear algebra might be helpful. The text is written in a style that is easy to follow and and manifolds book are superfluous examples/5(5).

This book presents the topology of surfaces, manifolds and knots in a manner that is reachable for undergraduate students with only a knowledge of calculus. Some linear algebra might be helpful. The text is written in a style that is easy to follow and there are superfluous examples/5. Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds.

A blend of examples and exercises leads the reader to anticipate general definitions and Price: $ book Topology of surfaces, knots, and manifolds: a first undergraduate course Stephan C Carlson Published in in New York NY) by Wiley. 4-Manifolds. Topology is only part of the story here.

Two books that focus on this part are: • M H Freedman and F Quinn. Topology of 4-Manifolds. Princeton University Press, [OP] • R E Gompf and A I Stipsicz. 4-Manifolds and Kirby Calculus. AMS, [$65] V. Miscelllaneous. • J Matouˇsek. Using the Borsuk-Ulam Theorem.

Springer File Size: 65KB. This title consists of a set of ideas and problems involving curves, surfaces and knots. Its aim is to introduce some basic ideas and problems concerning manifolds, especially one- and two-dimensional manifolds, via an intuition-based knots example-driven approach.

String topology is the study of algebraic and differential topological properties of spaces of paths and loops in Topology of surfaces. Topics covered includes: Intersection theory in loop spaces, The cacti operad, String topology as field theory, A Morse theoretic viewpoint, Brane topology.

Author(s): Ralph L. Cohen and Alexander A. Voronov. Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds.

General Topology by Shivaji University. This note covers the following topics: Topological spaces, Bases and subspaces, Special subsets, Different ways of defining topologies, Continuous functions, Compact spaces, First axiom space, Second axiom space, Lindelof spaces, Separable spaces, T0 spaces, T1 spaces, T2 – spaces, Regular spaces and T3 – spaces, Normal.

"Spaces of incompressible surfaces". This is an improved version of a paper published in Topology in with the title: "Homeomorphisms of sufficiently large P^2-irreducible 3-manifolds". pdf file (10 pages) "Triangulations of surfaces". The original version of this was published in Topology and its Applications in pdf file (7 pages).

Plot: Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds.

In topology, knot theory is the study of mathematical inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined together so that it cannot be undone, the simplest knot being a ring (or "unknot").In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space.

Knots and surfaces - the fascinating topology of n-manifolds Oxford Mathematician Andras Juhasz discusses and illustrates his latest research into knot theory.

"We can only see a small part of Space, even with the help of powerful telescopes. Informally, a manifold is a space that is "modeled on" Euclidean space.

There are many different kinds of manifolds, depending on the context. In geometry and topology, all manifolds are topological manifolds, possibly with additional structure, such as a differentiable structure.A manifold can be constructed by giving a collection of coordinate charts, that is a covering by.

Knots and surfaces. 4 () It surveys a specific area in Knot Theory concerning surfaces in knot exteriors. Some construction of small knots in small closed 3-manifolds are Author: Makoto Ozawa. Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds.

A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links--the objects of interest. Spanning Surfaces for Hyperbolic Knots in the 3-Sphere.

Colin C. Adams. as well as related topics including: three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology, hyperbolic knots and geometric structures of three.

contact structures on 3-manifolds. References: There is no required textbook, but occasionally I will give handouts in class. The following articles and books may also be useful: D. Rolfsen, "Knots and links." Publish or Perish, N. Saveliev, "Lectures on the topology of 3-manifolds." Berlin, New York: de Gruyter, Book Description.

This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.

David Mond, Some remarks on the geometry and classification of germs of maps from surfaces to 3-space, Topology 26 (), no. 3,DOI. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry.

However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. Get this from a library. Lectures on the Topology of 3-Manifolds: an Introduction to the Casson Invariant.

[Nikolai Saveliev] -- This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer.

Topology of surfaces 4. Examples of 3-manifolds 5. Basic knot theory Appendix Detailed Course Syllabi Remark: The presence of a text listed here is not meant to imply an endorsement of that text, nor is the absence of a particular text from the list meant to be an anti-endorsement.

Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as 4/5(1).

Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links.

Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than spectacular pictures, in the tradition of low-dimensional topology : World Scientific Publishing Company.

The completion of hyperbolic three-manifolds obtained from ideal polyhedra. 54 The generalized Dehn surgery invariant. 56 Dehn surgery on the figure-eight knot. 58 Degeneration of hyperbolic structures. 61 Incompressible surfaces in the figure-eight knot complement.

71 Thurston — The Geometry and Topology of 3 File Size: 1MB. The surface of a sphere and a 2-dimensional plane, both existing in some 3-dimensional space, are examples of what one would call surfaces. A topological manifold is the generalisation of this concept of a surface.

If every point in a topological space has a neighbourhood which is homeomorphic to an open subset of, for some non-negative integer, then the space is locally. The second central topic is topology of surfaces and classification of surfaces.

The main part of the course is learning about knots. One can imagine a knot as a continuous loop (e.g., made of very thin elastic rubber) in the three-dimensional space.

Abstract: This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics.

A Fête of Topology: Papers Dedicated to Itiro Tamura focuses on the progress in the processes, methodologies, and approaches involved in topology, including foliations, cohomology, and surface bundles. The publication first takes a look at leaf closures in Riemannian foliations and differentiable singular cohomology for foliations.

Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than spectacular pictures, in the tradition of low-dimensional topology books.Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level.

The next course the average stu­ dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition.