Geodesic
Geometric pushforward in Hodge filtered complex cobordism and secondary invariants
Documenta mathematica, Tome 29 (2024) no. 2, pp. 457-509

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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.
DOI : 10.4171/dm/951
Classification : 55N22, 14F43, 58J28, 19E15, 32C35
Mots-clés : cobordism, differential cohomology theories, Hodge filtered orientation, Thom morphism, Abel–Jacobi map 
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     author = {Knut Bjarte Haus and Gereon Quick},
     title = {Geometric pushforward in {Hodge} filtered complex cobordism and secondary invariants},
     journal = {Documenta mathematica},
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     year = {2024},
     doi = {10.4171/dm/951},
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Knut Bjarte Haus; Gereon Quick. Geometric pushforward in Hodge filtered complex cobordism and secondary invariants. Documenta mathematica, Tome 29 (2024) no. 2, pp. 457-509. doi: 10.4171/dm/951

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