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Reducibility of self-homotopy equivalences

Published online by Cambridge University Press:  26 March 2007

Petar Pavešić
Petar Pavešić*
Affiliation:
Fakulteta za Matematiko in Fiziko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenia (petar.pavesic@fmf.uni-lj.si)
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Abstract

We describe a new general method for the computation of the group Aut(X) of self-homotopy equivalences of a space. It is based on the decomposition of Aut(X) induced by a factorization of X into a product of simpler spaces. Normally, such decompositions require assumptions (‘induced equivalence property’, ‘diagonalizability’), which are strongly restrictive and difficult to check. We derive computable homological criteria for an analogous assumption, called reducibility, and then show that these criteria are satisfied when the so-called atomic decomposition of the space is used. This essentially reduces the computation of Aut(X) to the computation of the group of self-equivalences of its atomic factors, and the computation of certain homotopy sets between those factors.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 2 , 2007 , pp. 389 - 413
Copyright
Copyright © Royal Society of Edinburgh 2007

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