We study the homotopy type of finite-oriented Poincare' spaces (and, in particular, of closed topological manifolds) in even dimension. Our results relate polarized homotopy types over a stage of the Postnikov tower with the concept of CW-tower of categories due to Baues. This fact allows us to obtain a new formula for the top-dimensional obstruction for extending maps to homotopy equivalences. Then we complete the paper with an algebraic characterization of high-dimensional handlebodies
On the homotopy type of Poincare` spaces / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 180:(2001), pp. 331-358. [10.1007/s102310100015]
On the homotopy type of Poincare` spaces
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2001
Abstract
We study the homotopy type of finite-oriented Poincare' spaces (and, in particular, of closed topological manifolds) in even dimension. Our results relate polarized homotopy types over a stage of the Postnikov tower with the concept of CW-tower of categories due to Baues. This fact allows us to obtain a new formula for the top-dimensional obstruction for extending maps to homotopy equivalences. Then we complete the paper with an algebraic characterization of high-dimensional handlebodies
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