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 Trudy Mat. Inst. Steklova, 2010, Volume 268, Pages 76–93 (Mi tm2869)

Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class

Alexander A. Gaifullinab

a Moscow State University, Moscow, Russia
b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: The paper is devoted to the problem of finding explicit combinatorial formulae for the Pontryagin classes. We discuss two formulae, the classical Gabrielov–Gelfand–Losik formula based on investigation of configuration spaces and the local combinatorial formula obtained by the author in 2004. The latter formula is based on the notion of a universal local formula introduced by the author and on the usage of bistellar moves. We give a brief sketch for the first formula and a rather detailed exposition for the second one. For the second formula, we also succeed to simplify it by providing a new simpler algorithm for decomposing a cycle in the graph of bistellar moves of two-dimensional combinatorial spheres into a linear combination of elementary cycles.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 268, 70–86

Bibliographic databases:

UDC: 515.164.32

Citation: Alexander A. Gaifullin, “Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 76–93; Proc. Steklov Inst. Math., 268 (2010), 70–86

Citation in format AMSBIB
\Bibitem{Gai10} \by Alexander~A.~Gaifullin \paper Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class \inbook Differential equations and topology.~I \bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin \serial Trudy Mat. Inst. Steklova \yr 2010 \vol 268 \pages 76--93 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm2869} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2724336} \zmath{https://zbmath.org/?q=an:1227.57033} \elib{https://elibrary.ru/item.asp?id=13726636} \transl \jour Proc. Steklov Inst. Math. \yr 2010 \vol 268 \pages 70--86 \crossref{https://doi.org/10.1134/S0081543810010074} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000277345600007} \elib{https://elibrary.ru/item.asp?id=15332224} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952285837} 

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This publication is cited in the following articles:
1. D. A. Gorodkov, “A minimal triangulation of the quaternionic projective plane”, Russian Math. Surveys, 71:6 (2016), 1140–1142
2. Gorodkov D., “A 15-Vertex Triangulation of the Quaternionic Projective Plane”, Discret. Comput. Geom., 62:2 (2019), 348–373
3. Govc D., Marzantowicz W., Pavesic P., “How Many Simplices Are Needed to Triangulate a Grassmannian?”, Topol. Methods Nonlinear Anal., 56:2 (2020), 501–518
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