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 Andrew Ranicki - Oxford University Press
Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.
by C.T.C. Wall, A. A. Ranicki - American Mathematical Society
This book represents an attempt to collect and systematize the methods and main applications of the method of surgery, insofar as compact (but not necessarily connected, simply connected or closed) manifolds are involved.
by F.T. Farrell - Springer
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.
by Jonathan Hillman - arXiv
The goal of the book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such knots.