Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class
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.
Keywords
Cite
@article{arxiv.0912.3933,
title = {Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class},
author = {Alexander A. Gaifullin},
journal= {arXiv preprint arXiv:0912.3933},
year = {2024}
}
Comments
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. Institute