Towards a Classification of Almost Complex and Spin^h Manifolds

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dc.contributor.advisorRosenberg, Jonathanen_US
dc.contributor.authorMills, Keithen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2024-06-29T05:38:43Z
dc.date.available2024-06-29T05:38:43Z
dc.date.issued2024en_US
dc.description.abstractWe show that all homotopy CP^ns, smooth closed manifolds with the oriented homotopy type of CP^n, admit almost complex structures for 3 ≤ n ≤ 6, and classify these structures by their Chern classes for n=4, 6. Our methods provide a new proof of a result of Libgober and Wood on the classification of almost complex structures on homotopy CP^4s. We also show that all homotopy RP^(2k+1)s admit stably almost complex structures. Spin^h manifolds are the quaternionic analogue to spin^c manifolds. At the prime 2 we compute the spin^h bordism groups by proving a structure theorem for the cohomology of the spin^h bordism spectrum MSpin^h as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting of MSpin^h as a wedge sum of familiar spectra. We also compute the decomposition of H^*(MSpin^h; Z/2Z) explicitly in degrees up through 30 via a counting process.en_US
dc.identifierhttps://doi.org/10.13016/c4lx-sxp4
dc.identifier.urihttp://hdl.handle.net/1903/32867
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledTheoretical mathematicsen_US
dc.subject.pqcontrolledGender studiesen_US
dc.subject.pquncontrolledAlmost Complexen_US
dc.subject.pquncontrolledGeometric Topologyen_US
dc.subject.pquncontrolledHomotopyen_US
dc.subject.pquncontrolledManifoldsen_US
dc.subject.pquncontrolledSurgery Theoryen_US
dc.subject.pquncontrolledTopologyen_US
dc.titleTowards a Classification of Almost Complex and Spin^h Manifoldsen_US
dc.typeDissertationen_US

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