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
Recommended Citation
Ghosh, Sudipta, "Connected Sums and Directed Systems in Knot Floer Homologies" (2022). LSU Doctoral Dissertations. 5923.
https://repository.lsu.edu/gradschool_dissertations/5923
Committee Chair
Vela-Vick, David Shea
DOI
10.31390/gradschool_dissertations.5923