by Louis H. Kauffman
Publisher: arXiv 2004
Number of pages: 107
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.
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by S. Hong, J. Kalliongis, D. McCullough, J. H. Rubinstein - arXiv
The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature. For any elliptic 3-manifold M, the inclusion from the isometry group of M to the diffeomorphism group of M is a homotopy equivalence.
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This is a textbook on differential forms. The primary target audience is sophomore level undergraduates enrolled in a course in vector calculus. Later chapters will be of interest to advanced undergraduate and beginning graduate students.
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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.
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The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory.