The Surgery Exact Triangle in Monopole Floer Homology with Z[i] Coefficients
Name
freeman-freemanj-phd-mathematics-2021-thesis.pdf
Description
Thesis PDF
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4.59 MB
Format
Adobe PDF
Checksum (MD5)
cd1e21e55d46244b8243f80876e0483e
Author(s)
Freeman, Jesse
Advisor(s)
Mrowka, Tomasz
Date Issued
June 2021
Publisher
Massachusetts Institute of Technology
Abstract
In their seminal paper, Kronheimer, Mrowka, Ozsváth and Szabó, establish the existence of a surgery exact triangle for Monopole Floer homology. The triangle was a theoretical breakthrough and allowed us to answer questions about the surgery correspondence between knots and 3-manifolds that were previously mysterious. A serious limitation of their triangle was that it only holds over characteristic two. In this paper, we establish the existence of a surgery exact triangle using local coefficients valued in Z[i].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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