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Foundations of geometric cohomology: from co-orientations to product structures

· 2022 · math.AT · arXiv 2212.07482

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abstract

This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product of such smooth maps, which provides our geometric cochains with a partially defined product structure inducing the cup product in cohomology. A parallel treatment of homology is also given allowing for a geometric unification of the contravariant and covariant theories.

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The transverse singular complex

math.AT · 2026-04-30 · unverdicted · novelty 7.0

Sing(M) deformation retracts onto the transverse singular subcomplex Sing^T(M) when T is countable.

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  • The transverse singular complex math.AT · 2026-04-30 · unverdicted · none · ref 1 · internal anchor

    Sing(M) deformation retracts onto the transverse singular subcomplex Sing^T(M) when T is countable.