In this paper we describe some relations between various structure sets which arise naturally for a Browder-Livesay filtration of a closed topological manifold. We use the algebraic surgery theory of Ranicki for realizing the surgery groups and natural maps on the spectrum level. We obtain also new relations between Browder-Quinn surgery obstruction groups and structure sets. Finally we illustrate several examples and applications.
On the Surgery Theory for Filtered Manifolds / Cavicchioli, Alberto; Hegenbarth, Friedrich; Yuri, Muranov; Spaggiari, Fulvia. - In: MATHEMATICS AND STATISTICS. - ISSN 2332-2071. - STAMPA. - 1 (4):(2013), pp. 204-219. [10.13189/ms.2013.010405]
On the Surgery Theory for Filtered Manifolds
CAVICCHIOLI, Alberto;HEGENBARTH, FRIEDRICH;SPAGGIARI, Fulvia
2013
Abstract
In this paper we describe some relations between various structure sets which arise naturally for a Browder-Livesay filtration of a closed topological manifold. We use the algebraic surgery theory of Ranicki for realizing the surgery groups and natural maps on the spectrum level. We obtain also new relations between Browder-Quinn surgery obstruction groups and structure sets. Finally we illustrate several examples and applications.
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