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We present a local combinatorial formula for Euler class of $n$-dimensional PL spherical fiber bundle as a rational number $e_{it CH}$ associated to chain of $n+1$ abstract subdivisions of abstract $n$-spherical PL cell complexes. The number $e_{it CH}$ is combinatorial (or matrix) Hodge theory twisting cochain in Guy Hirshs homology model of the bundle associated with PL combinatorics of the bundle.
Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklac
We give a local Euler-Maclaurin formula for rational convex polytopes in a rational euclidean space . For every affine rational polyhedral cone C in a rational euclidean space W, we construct a differential operator of infinite order D(C) on W with c
Pure combinatorial models for BPL_n and Gauss map of a combinatorial manifold are described.
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double ex
We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with $mathbb{R}$-coefficients). This complements Filipazzis canonical bundle formula for morphisms with connected fibres. It is then applied to