The Surgery Exact Triangle in Monopole Floer Homology with Z[i] Coefficients

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].

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2021

Author dc:creator

• Freeman, Jesse

Advisor dc:contributor.advisor

• Mrowka, Tomasz

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/139100

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/139100