Geometric Topology: Localization, Periodicity and Galois Symmetry
by Dennis Sullivan
Publisher: Springer 2005
Number of pages: 296
In 1970, Sullivan circulated a set of notes introducing localization and completion of topological spaces to homotopy theory, and other important concepts that have had a major influence on the development of topology. The notes remain worth reading for the boldness of their ideas, the clear mastery of available structure they command, and the fresh picture they provide for geometric topology.
Download or read it online for free here:
by Frank Quinn, Andrew Ranicki
Homology manifolds were developed in the 20th century to give a precise setting for Poincare's ideas on duality. They are investigated using algebraic and geometric methods. This volume is the proceedings of a workshop held in 2003.
by Ralph L. Cohen, Alexander A. Voronov - arXiv
This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research.
by Eiji Ogasa - arXiv
This is an introductory article on high dimensional knots for the beginners. Is there a nontrivial high dimensional knot? We first answer this question. We explain local moves on high dimensional knots and the projections of high dimensional knots.
by Louis H. Kauffman - arXiv
This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.