We prove a decomposition theorem for closed connected homotopy equivalent smooth four-manifolds, which partially extends a recent result of Curtis et al. (1996) to the non-simply connected case. Then we study the question of when a homotopy equivalence between closed smooth 4-manifolds is homotopic to a topological homeomorphism. In particular, we obtain a new proof of the well-known uniqueness of closed aspherical smooth 4-manifolds with good fundamental groups.
A splitting theorem for homotopy equivalent smooth 4-manifolds / Cavicchioli, Alberto; F., Hegenbarth; Spaggiari, Fulvia. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 1120-7183. - STAMPA. - 17 Serie VII:(1997), pp. 523-539.
A splitting theorem for homotopy equivalent smooth 4-manifolds
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
1997
Abstract
We prove a decomposition theorem for closed connected homotopy equivalent smooth four-manifolds, which partially extends a recent result of Curtis et al. (1996) to the non-simply connected case. Then we study the question of when a homotopy equivalence between closed smooth 4-manifolds is homotopic to a topological homeomorphism. In particular, we obtain a new proof of the well-known uniqueness of closed aspherical smooth 4-manifolds with good fundamental groups.
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