Glasnik Matematicki, Vol. 42, No.1 (2007), 131-144.

A SPECTRAL SEQUENCE FOR THE GROUP OF SELF-MAPS WHICH INDUCE INDENTITY AUTOMORPHISMS OF HOMOLOGY GROUPS

Petar Pavešić

Abstract.   Let Aut_*(X) denote the group of homotopy classes of self-maps of X which induce identity automorphisms of homology groups. We construct a spectral sequence converging to Aut_*(X), induced by the cellular decomposition of X, and use it to obtain some structural and computational results.

2000 Mathematics Subject Classification.   55P10.

Key words and phrases.   Self-homotopy equivalence, cellular decomposition, spectral sequence, Cartan-Eilenberg method, nilpotent group, localization.

DOI: 10.3336/gm.42.1.11

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