Hodge filtered complex bordism

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 $\A^1$-homotopy invariance. Moreover, we obtain transfer maps along projective morphisms.

minor revision; final version accepted for publication by the Journal of Topology

References in corpus (2)

• Algebras and modules in monoidal model categories
• Equivalences of monoidal model categories

Cited by in corpus (7)

• Symmetric operads in abstract symmetric spectra
• Regulators and cycle maps in higher-dimensional differential algebraic K-theory
• Higher Topos Theory in Physics
• Twisted smooth Deligne cohomology
• Differential cohomology (encyclopedia article)
• Unstable splittings in Hodge filtered Brown-Peterson cohomology
• Steenrod operations and algebraic classes