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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)70-86
Number of pages17
JournalProceedings of the Steklov Institute of Mathematics
Volume268
Issue number1
DOIs
Publication statusPublished - 2010
Externally publishedYes

Fingerprint

Dive into the research topics of 'Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class'. Together they form a unique fingerprint.

Cite this