Configuration spaces,bistellar moves,and combinatorial formulae for the first Pontryagin class |
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Authors: | Alexander A Gaifullin |
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Institution: | (1) City University of New York Brooklyn College, Bedford Avenue 2900, 11210-2889 Brooklyn, New York, USA |
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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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Keywords: | |
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