( 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.