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dc.contributor.advisorQuick, Gereon
dc.contributor.advisorThaule, Marius
dc.contributor.authorHaus, Knut Bjarte
dc.date.accessioned2022-09-13T10:54:51Z
dc.date.available2022-09-13T10:54:51Z
dc.date.issued2022
dc.identifier.isbn978-82-326-6205-0
dc.identifier.issn2703-8084
dc.identifier.urihttps://hdl.handle.net/11250/3017489
dc.description.abstractWe 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.isoengen_US
dc.publisherNTNUen_US
dc.relation.ispartofseriesDoctoral theses at NTNU;2022:238
dc.titleGeometric Hodge filtered complex cobordismen_US
dc.typeDoctoral thesisen_US
dc.subject.nsiVDP::Mathematics and natural science: 400::Mathematics: 410en_US
dc.description.localcodeDigital fulltext is not availableen_US


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