Exotic Homology Manifolds
by Frank Quinn, Andrew Ranicki
Number of pages: 158
Homology manifolds were developed in the first half of the 20th century to give a precise setting for Poincare's ideas on duality. Exotic homology manifolds are investigated using algebraic and geometric methods. This volume is the proceedings of the Mini-Workshop Exotic Homology manifolds held at Oberwolfach 2003.
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by Louis H. Kauffman - University of Illinois at Chicago
This book is an introduction to knot theory and to Witten's approach to knot theory via his functional integral. Contents: Topics in combinatorial knot theory; State Models and State Summations; Vassiliev Invariants and Witten's Functional Integral.
by R. Fenn, D.P. Ilyutko, L.H. Kauffman, V.O. Manturov - arXiv
The purpose of this paper is to give an introduction to virtual knot theory and to record a collection of research problems that the authors have found fascinating. The paper introduces the theory and discusses some problems in that context.
by Danny Calegari - Oxford University Press
The book gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms, and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
by S.Chmutov, S.Duzhin, J.Mostovoy - Ohio State Universit
An introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. Written for readers with no background in this area, and we care more about the basic notions than about more advanced material.