An Introduction to High Dimensional Knots
by Eiji Ogasa
Publisher: arXiv 2013
Number of pages: 92
This is an introductory article on high dimensional knots for the beginners. Is there a nontrivial high dimensional knot? We first answer this question. After that, we explain local moves on high dimensional knots and the projections of high dimensional knots.
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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.
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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.
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This book is an introduction to the topological rigidity theorem for compact non-positively curved Riemannian manifolds. It contains a quick informal account of the background material from surgery theory and controlled topology prerequesite.
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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.