Geometric pushforward in Hodge filtered complex cobordism and secondary invariants

  • Knut Bjarte Haus

    Norwegian University of Science and Technology, Trondheim, Norway
  • Gereon Quick

    Norwegian University of Science and Technology, Trondheim, Norway
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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.

Cite this article

Knut Bjarte Haus, Gereon Quick, Geometric pushforward in Hodge filtered complex cobordism and secondary invariants. Doc. Math. 29 (2024), no. 2, pp. 457–509

DOI 10.4171/DM/951