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Zap. Nauchn. Sem. POMI, 2007, Volume 344, Pages 56–173 (Mi znsl104)  

This article is cited in 1 scientific paper (total in 1 paper)

Combinatorial PL fiber bundles and fragmentation of a fiberwise homeomorphism

N. E. Mnev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: Among other things, we prove that for any compact PL-manifold $X$ there is a homotopy equivalence $BPL(X)\approx BT(X)$, where $T(X)$ is the category of abstract aggregations of triangulations of $X$. As a result, we get a functorial pure combinatorial models for PL fiber bundles. Special attention is paid to the case $X=\mathbb R^n$ and the combinatorial model of the Gauss map of a combinatorial manifold. The key trick which makes the proof possible is a collection of lemmas describing the fragmentation of a fiberwise homeomorphism.

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English version:
Journal of Mathematical Sciences (New York), 2007, 147:6, 7155–7217

Bibliographic databases:

UDC: 515.14
Received: 02.05.2007

Citation: N. E. Mnev, “Combinatorial PL fiber bundles and fragmentation of a fiberwise homeomorphism”, Representation theory, dynamical systems, combinatorial methods. Part XV, Zap. Nauchn. Sem. POMI, 344, POMI, St. Petersburg, 2007, 56–173; J. Math. Sci. (N. Y.), 147:6 (2007), 7155–7217

Citation in format AMSBIB
\Bibitem{Mne07}
\by N.~E.~Mnev
\paper Combinatorial PL fiber bundles and fragmentation of a~fiberwise homeomorphism
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XV
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 344
\pages 56--173
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl104}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2432169}
\elib{http://elibrary.ru/item.asp?id=9595478}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 147
\issue 6
\pages 7155--7217
\crossref{https://doi.org/10.1007/s10958-007-0537-z}
\elib{http://elibrary.ru/item.asp?id=13549683}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36148953859}


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    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 200:6 (2014), 710–717  mathnet  crossref
  • Записки научных семинаров ПОМИ
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