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Mat. Sb., 2008, Volume 199, Number 6, Pages 3–26 (Mi msb3904)  

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

Full text: PDF file (661 kB)
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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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  • https://doi.org/10.4213/sm3904
  • http://mi.mathnet.ru/eng/msb/v199/i6/p3

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Cavicchioli, Yu. V. Muranov, F. Spaggiari, F. Hegenbarth, “On Iterated Browder–Livesay Invariants”, Math. Notes, 86:2 (2009), 196–215  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Bak A., Muranov Y.V., “Surgery on a pair of transversal manifolds”, J. Homotopy Relat. Struct, 7:2 (2012), 255–279  crossref  mathscinet  zmath  isi  scopus
    3. Hegenbarth F., Muranov Yu.V., Repovs D., “Surgery in Codimension 3 and the Browder-Livesay Invariants”, Turk. J. Math., 37:5 (2013), 806–817  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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