Manifolds with Highly Connected Universal Covers

Cavicchioli, Alberto; Hegenbarth, Friedrich

doi:10.1007/978-3-0348-9018-2_5

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A Review On a Theorem Of Jh Baues1

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2001

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“…Observe that P 2 (π) contains all 4-dimensional Poincaré complexes (and, of course, all closed topological 4-manifolds) with fundamental group π. For algebraic characterizations of aspherical manifolds in P n (π), and results on the minimality of their Euler characteristics we refer to [8].…”

Section: A Review On a Theorem Of Jh Bauesmentioning

confidence: 99%

On the homotopy type of Poincaré spaces

Cavicchioli

Spaggiari

2001

Ann. Mat. Pura Appl. IV. Ser.

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We study the homotopy type of finite-oriented Poincaré 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.Mathematics Subject Classification (1991). 57N65, 57R67

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Section: A Review On a Theorem Of Jh Bauesmentioning

confidence: 99%