Geometry and Topology : Manifolds: Varieties, and Knots book cover
1st Edition

Geometry and Topology
Manifolds: Varieties, and Knots

ISBN 9781138430310
Published August 2, 2017 by CRC Press
368 Pages

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Book Description

This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.

Table of Contents

1. Introduction to resolution towers 2. A geometric construction of the boundedly controlled Whitehead group 3. An introduction to boundedly controlled simple homotopy theory 4. On certain branched cyclic covers of S3 5. A geometric interpretation of Siebenmann’s periodicity phenomenon 6. Regular convex cell complexes 7. Gauge theory and smooth structures on 4-manifolds 8. Algebraic varieties which arc a disjoint union of subvarieties 9. The lower central series of generalized pure braid groups 10. Implication of the geometrization conjecture for the algebraic K-theory of 3-manifolds 11. On the diffeomorphism types of certain elliptic surfaces 12. Deformations of flat bundles over Kahler manifolds 13. Imbeddings of knot groups in knot groups 14. Geometric Hopfian and non-Hopfian situations 15. Deformations of totally geodesic foliations 16. Automorphisms of punctured-surface bundles 17. Lattice gauge fields and Chern-Weil theory 18. Intrinsic skeleta and intersection homology of weakly stratified sets 19. Isolated critical points of maps from R4 to R2 and a natural splitting of the Milnor number of a classical fibred link, part II 20. Covering theorems for open surfaces 21. Equivaniant handles in finite group actions 22. The role of knot theory in DNA research 23. Continuous versus discrete symmetry 24. The knotting of theta curves and other graphs in S3

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