Geometric Hodge filtered complex cobordism
Algebraic Topology
2023-08-01 v2 Complex Variables
Differential Geometry
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.
Keywords
Cite
@article{arxiv.2210.13259,
title = {Geometric Hodge filtered complex cobordism},
author = {Knut Bjarte Haus and Gereon Quick},
journal= {arXiv preprint arXiv:2210.13259},
year = {2023}
}
Comments
46 pages, minor revision, v2 is the final version accepted for publication in Advances in Mathematics