The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds
by A.A. Ranicki, et al,
Publisher: Springer 1996
Number of pages: 194
The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that further development of high-dimensional topology would lead to a verification in all dimensions.
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by Andrew Ranicki - Cambridge University Press
This is the first treatment of the applications of the lower K- and L-groups to the topology of manifolds such as Euclidean spaces, via Whitehead torsion and the Wall finiteness and surgery obstructions. Only elementary constructions are used.
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.
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.
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.