A note on a local combinatorial formula for the Euler class of a PL spherical fiber bundle

Nikolai Mnëv

paper

A note on a local combinatorial formula for the Euler class of a PL spherical fiber bundle

arXiv:2109.06143

Abstract

We present a local combinatorial formula for the Euler class of a $n$ -dimen\-si\-onal PL spherical fiber bundle as a rational number $e_{CH}$ associated to a chain of $n + 1$ abstract subdivisions of abstract $n$ -spherical PL cell complexes. The number $e_{CH}$ is a combinatorial (or matrix) Hodge theory twisting cochain in Guy Hirsch's homology model of the bundle associated with PL combinatorics of the bundle.