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This article is cited in 3 scientific papers (total in 3 papers)
Splitting a simple homotopy equivalence along a submanifold with filtration
A. Baka, Yu. V. Muranovb a Bielefeld University
b Universidad Tecnológica de la Mixteca
Abstract:
A simple homotopy equivalence $f\colon M^n\to X^n$ of manifolds splits along a submanifold $Y\subset X$ if it is homotopic to a map that is a simple homotopy equivalence on the transversal preimage of the submanifold and on the complement of this preimage. The problem of splitting along a submanifold with filtration is a natural generalization of this problem. In this paper we define groups $\mathit{LSF}_*$ of obstructions to splitting along a submanifold with filtration and describe their properties. We apply the results obtained to the problem of the realization of surgery and splitting obstructions by maps of closed manifolds and consider several examples.
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DOI:
https://doi.org/10.4213/sm3904
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English version:
Sbornik: Mathematics, 2008, 199:6, 787–809
Bibliographic databases:
UDC:
515.163+515.164.22+515.14
MSC: Primary 57R67; Secondary 19J25 Received: 05.06.2007
Citation:
A. Bak, Yu. V. Muranov, “Splitting a simple homotopy equivalence along a submanifold with filtration”, Mat. Sb., 199:6 (2008), 3–26; Sb. Math., 199:6 (2008), 787–809
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/msb3904https://doi.org/10.4213/sm3904 http://mi.mathnet.ru/eng/msb/v199/i6/p3
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This publication is cited in the following articles:
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A. Cavicchioli, Yu. V. Muranov, F. Spaggiari, F. Hegenbarth, “On Iterated Browder–Livesay Invariants”, Math. Notes, 86:2 (2009), 196–215
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Bak A., Muranov Y.V., “Surgery on a pair of transversal manifolds”, J. Homotopy Relat. Struct, 7:2 (2012), 255–279
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Hegenbarth F., Muranov Yu.V., Repovs D., “Surgery in Codimension 3 and the Browder-Livesay Invariants”, Turk. J. Math., 37:5 (2013), 806–817
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