ABSTRACT HOMOTOPY & SIMPLE HOMOTOPY THE

The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).

List of contents

Abstract Homotopy Theory; Case Studies; Exact Sequences; Elementary Homotopy Coherence; Abstract Simple Homotopy Theory; Additive Simple Homotopy Theories.

Product details

• Authors: Kamps K Heiner, T Porter K H Kamps, K H Kamps, K Heiner (Fern Univ Kamps, K. H. Kamps, K. Heiner Kamps, T. Porter, Timothy Porter, Timothy (Univ Of Wales Bangor Porter
• Publisher: World Scientific
• Languages: English
• Product format: Hardback
• Released: 11.04.1997
• EAN: 9789810216023
• ISBN: 978-981-02-1602-3
• No. of pages: 474
• Dimensions: 157 mm x 235 mm x 30 mm
• Weight: 831 g
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry