Monopoles and Pin(2)-symmetry
Author(s)Lin, Francesco Ph. D. Massachusetts Institute of Technology
Monopoles and Pin(two)-symmetry
Massachusetts Institute of Technology. Department of Mathematics.
Tomasz S. Mrowka.
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In this thesis we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a spinc structure which is isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture. Furthermore, we discuss the analogue in this setting of the surgery exact triangle, and perform some sample computations.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 321-326).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology