Mathematics and Statistics Vol. 1(4), pp. 204 - 219
DOI: 10.13189/ms.2013.010405
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On the Surgery Theory for Filtered Manifolds

Alberto Cavicchioli ^1,*, Friedrich Hegenbarth ², Yurij V. Muranov ³, Fulvia Spaggiari ^1
1 Dipartimento di Scienze Fisiche, Informatiche e Matematiche Universit`a di Modena e Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy
² Dipartimento di Matematica, Università di Milano, Via Saldini n. 50, 20133 Milano, Italy
³ Department of Mathematics, Grodno State University, Ozheshko str. 22, 230023 Grodno, Belarus

ABSTRACT

In this paper we describe some relations between various structure sets which arise naturally for a Browder-Livesay ltration of a closed topological mani- fold. 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.

KEYWORDS
Surgery on manifolds, Browder-Livesay ltration, Browder-Quinn surgery obstruction groups, Surgery on stratied manifolds, Splitting obstruction groups, Surgery exact sequence, Structure sets, Normal invariants

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Alberto Cavicchioli , Friedrich Hegenbarth , Yurij V. Muranov , Fulvia Spaggiari , "On the Surgery Theory for Filtered Manifolds," Mathematics and Statistics, Vol. 1, No. 4, pp. 204 - 219, 2013. DOI: 10.13189/ms.2013.010405.

(b). APA Format:
Alberto Cavicchioli , Friedrich Hegenbarth , Yurij V. Muranov , Fulvia Spaggiari (2013). On the Surgery Theory for Filtered Manifolds. Mathematics and Statistics, 1(4), 204 - 219. DOI: 10.13189/ms.2013.010405.