dc.contributor.advisor | Quick, Gereon | |
dc.contributor.advisor | Thaule, Marius | |
dc.contributor.author | Haus, Knut Bjarte | |
dc.date.accessioned | 2022-09-13T10:54:51Z | |
dc.date.available | 2022-09-13T10:54:51Z | |
dc.date.issued | 2022 | |
dc.identifier.isbn | 978-82-326-6205-0 | |
dc.identifier.issn | 2703-8084 | |
dc.identifier.uri | https://hdl.handle.net/11250/3017489 | |
dc.description.abstract | We define geometric Hodge filtered complex cobordism groups MUn(p)(X) for complex manifolds X. Refining the Pontryagin–Thom construction, we give a natural isomorphism MUn(p)(X) ƒ MUnD (p)(X), where MUnD(p)(X) are the Hodge filtered complex cobordism groups defined in [30]. We establish a pushforward map gú : MUn(p)(X) æ MUn+2d(p + d)(Y ) for each proper holomorphic map g : X æ Y . Using gú, we get for algebraic manifolds X a map !n alg(X) æ MU2n(n)(X), where !n alg(X) denotes the algebraic cobordism group of X. This induces an Abel–Jacobi map. Using a cycle model for Deligne-cohomology similar to that of [21], we describe the Thom-morphism MUn(p)(X) æ HnD (X; Z(p)), and verify that our Abel–Jacobi map refines that of Gri!ths. | |
dc.language.iso | eng | en_US |
dc.publisher | NTNU | en_US |
dc.relation.ispartofseries | Doctoral theses at NTNU;2022:238 | |
dc.title | Geometric Hodge filtered complex cobordism | en_US |
dc.type | Doctoral thesis | en_US |
dc.subject.nsi | VDP::Mathematics and natural science: 400::Mathematics: 410 | en_US |
dc.description.localcode | Digital fulltext is not available | en_US |