English

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 \A1\A^1-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

R2 v1 2026-06-21T22:51:47.750Z