Hodge filtered complex bordism
Algebraic Topology
2017-05-17 v3 Algebraic Geometry
Differential Geometry
Abstract
We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show that the theory satisfies a projective bundle formula and -homotopy invariance. Moreover, we obtain transfer maps along projective morphisms.
Keywords
Cite
@article{arxiv.1212.2173,
title = {Hodge filtered complex bordism},
author = {Michael J. Hopkins and Gereon Quick},
journal= {arXiv preprint arXiv:1212.2173},
year = {2017}
}
Comments
minor revision; final version accepted for publication by the Journal of Topology