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dc.contributor.advisor Stong, Richard
dc.creatorClark, Gregory Sterling
dc.date.accessioned 2009-06-04T08:19:42Z
dc.date.available 2009-06-04T08:19:42Z
dc.date.issued 2001
dc.identifier.urihttps://hdl.handle.net/1911/17948
dc.description.abstract Given a notion of equivalence of 4-manifolds, there is a corresponding notion of stable equivalence: M is stably equivalent to N if M#rS2 x S2 is equivalent to N# sS2 x S2 for some non-negative integers r, s. Any equivalence relation which extends over an S2 x S2 summand gives a well-defined equivalence relation, and homotopy equivalence is such a relation. In this paper, we examine how the invariant sec of a 4-manifold M with finite fundamental group and spin universal cover relates to the stable homotopy type of M. The sec invariant of a manifold M may be defined in terms of a characteristic 3-dimensional homology class w2 + w on a null-cobordism of M. In the case where sec = 0, we are able to conclude some geometric information about w2 + w; namely, that w 2 + w is represented by S3 . This allows us to prove that sec (M) determines the stable homotopy type of M, or more generally, that manifolds M and N for which sec (M - N) is defined and equal to 0, are stably homotopy equivalent. We also prove a partial converse to this theorem. If M and N are homotopy equivalent, and there exists a homeomorphism M# C P2 → N# C P2 which preserves the homotopy classes of the core 2-spheres of the C P2, then sec (M - N) = 0.
dc.format.extent 57 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title Stable homotopy invariance of Teichner's sec invariant
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Clark, Gregory Sterling. "Stable homotopy invariance of Teichner's sec invariant." (2001) Diss., Rice University. https://hdl.handle.net/1911/17948.


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