Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory
by R. Fenn, D.P. Ilyutko, L.H. Kauffman, V.O. Manturov
Publisher: arXiv 2014
Number of pages: 66
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 second section of the paper introduces the theory and discusses some problems in that context.
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by Allen Hatcher
These pages are really just an early draft of the initial chapters of a real book on 3-manifolds. The text does contain a few things that aren't readily available elsewhere, like the Jaco-Shalen/Johannson torus decomposition theorem.
by John R. Stallings - Tata Institute of Fundamental Research
These notes contain: The elementary theory of finite polyhedra in real vector spaces; A theory of 'general position' (approximation of maps), based on 'non-degeneracy'. A theory of 'regular neighbourhoods' in arbitrary polyhedra; etc.
by Nigel Hitchin
Geometry of Surfaces by Nigel Hitchin is a textbook on surfaces. However the author is also going to try and consider surfaces intrinsically, or abstractly, and not necessarily embedded in three-dimensional Euclidean space.
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.