Reducibility of Self-homotopy Equivalences
نویسنده
چکیده
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 hard to check. In this paper we derive computable homological criteria for an analogous assumption, called reducibility, and then show that those 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.
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