Geometric pushforward in Hodge filtered complex cobordism and secondary invariants
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917577272328192 |
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| author | Haus, Knut Bjarte Quick, Gereon |
| author_facet | Haus, Knut Bjarte Quick, Gereon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15899 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric pushforward in Hodge filtered complex cobordism and secondary invariants Haus, Knut Bjarte Quick, Gereon Algebraic Topology Algebraic Geometry Complex Variables K-Theory and Homology 55N22, 14F43, 58J28, 19E15, 32C35 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. |
| title | Geometric pushforward in Hodge filtered complex cobordism and secondary invariants |
| topic | Algebraic Topology Algebraic Geometry Complex Variables K-Theory and Homology 55N22, 14F43, 58J28, 19E15, 32C35 |
| url | https://arxiv.org/abs/2303.15899 |