Twisted Manolescu-Floer spectra for Seiberg-Witten monopoles
Massachusetts Institute of Technology. Department of Mathematics.
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In this thesis, we extend Manolescus and Kronheimer-Manolescus construction of Floer homotopy type to general 3-manifolds. This Floer homotopy type is a candidate for an object whose suitable homology groups recover Floer homology. The main idea is to apply finite dimensional approximation technique and Conley index theory to Seiberg-Witten theory of 3-manifolds. Another part of the construction involves a concept of twisted parametrized spectra introduced by Douglas. We also provide explicit computation for the manifolds S 1 x S 2 and T 3 .
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 123-125).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology