Geometric pushforward in Hodge filtered complex cobordism and secondary invariants
Journal article, Peer reviewed
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Date
2024Metadata
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- Institutt for matematiske fag [2530]
- Publikasjoner fra CRIStin - NTNU [38685]
Abstract
We construct a functorial pushforward homomorphism in geometric Hodge filtered complex cobordism along proper holomorphic maps between arbitrary complex manifolds. This significantly improves previous results on such transfer maps and is a much stronger result than the ones known for differential cobordism of smooth manifolds. This enables us to define and provide a concrete geometric description of Hodge filtered fundamental classes for all proper holomorphic maps. Moreover, we give a geometric description of a cobordism analog of the Abel–Jacobi invariant for nullbordant maps which is mapped to the classical invariant under the Hodge filtered Thom morphism. For the latter we provide a new construction in terms of geometric cycles.