Tautological classes of definite 4-manifolds

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dc.contributor.authorBaraglia, D.
dc.date.issued2023
dc.description.abstractWe prove a diagonalisation theorem for the tautological, or generalised Miller–Morita– Mumford, classes of compact, smooth, simply connected, definite 4–manifolds. Our result can be thought of as a families version of Donaldson’s diagonalisation theorem. We prove our result using a families version of the Bauer–Furuta cohomotopy refinement of Seiberg–Witten theory. We use our main result to deduce various results concerning the tautological classes of such 4–manifolds. In particular, we completely determine the tautological rings of CP2 and CP2 # CP2 . We also derive a series of linear relations in the tautological ring which are universal in the sense that they hold for all compact, smooth, simply connected definite 4–manifolds.
dc.description.statementofresponsibilityDavid Baraglia
dc.identifier.citationGeometry and Topology, 2023; 27(2):641-698
dc.identifier.doi10.2140/gt.2023.27.641
dc.identifier.issn1364-0380
dc.identifier.issn1364-0380
dc.identifier.orcidBaraglia, D. [0000-0002-8450-1165]
dc.identifier.urihttps://hdl.handle.net/2440/138803
dc.language.isoen
dc.publisherMathematical Sciences Publishers
dc.relation.granthttp://purl.org/au-research/grants/arc/DP170101054
dc.rights© 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.
dc.source.urihttps://doi.org/10.2140/gt.2023.27.641
dc.subjecttautological classes; Miller–Morita–Mumford classes; Seiberg–Witten; Bauer–Furuta; definite 4–manifolds
dc.titleTautological classes of definite 4-manifolds
dc.typeJournal article
pubs.publication-statusPublished

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