Geometric Hodge filtered complex cobordism

Knut Bjarte Haus; Gereon Quick

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arXiv · 2210.13259

Geometric Hodge filtered complex cobordism

Knut Bjarte Haus·Gereon Quick

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Abstract

We construct a geometric cycle model for a Hodge filtered extension of complex cobordism for every smooth manifold with a filtration on its de Rham complex with complex coefficients. Using a refinement of the Pontryagin-Thom construction, we construct an explicit isomorphism between our geometric model and the abstract model of Hodge filtered complex cobordism of Hopkins-Quick for every complex manifold with the Hodge filtration.

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Knut Bjarte Haus, Gereon Quick. 2022-10-24. Geometric Hodge filtered complex cobordism. https://arxiv.org/abs/2210.13259

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