188 research outputs found
Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class
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.Comment: 18 pages, 4 LaTeX pseudofigures, Talk at conference dedicated to the
Centennial Anniversary of L.S. Pontryagin (Moscow, 2008), to appear in Proc.
Steklov Math. Institut
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