Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

This thesis proves a connected sum formula for Heegaard, instanton and monopole knot Floer homologies defined using direct limits. Our techniques rely on Sutured Floer theories and the contact gluing maps. Along the way, we prove several folklore results about the Honda-Kazez-Mati\'{c} gluing map in Heegaard Floer homology. As an application of our argument we deduce the oriented skein exact triangle for Heegaard, instanton and monopole knot Floer homology.

Date

7-20-2022

Committee Chair

Vela-Vick, David Shea

Available for download on Monday, July 09, 2029

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