Surgery Exact Triangles in Instanton Theory
Name
bhat-deeparaj-phd-mathematics-2024-thesis.pdf
Description
Thesis PDF
Size
803.73 KB
Format
Adobe PDF
Checksum (MD5)
969bbdceb57a65f38da152d8f3c42181
Author(s)
Bhat, Deeparaj
Advisor(s)
Mrowka, Tomasz
Date Issued
September 2024
Publisher
Massachusetts Institute of Technology
Abstract
The introduction of instanton Floer theory and Donaldson polynomial invariants in the 1980s revolutionised the study of low dimensional topology. Since then, many Floer theories have been introduced with different structural properties and qualitative features. One of these Floer theories, Heegaard Floer theory, is popular due to its computational ease and rich algebraic structure. One of the computational tools absent in other Floer theories is the integer surgery formula that computes Heegaard Floer homology of 3-manifolds obtained by surgery along knot(s) in them. This thesis establishes a new surgery formula in instanton Floer theory. The algebraic language to express this formula is that of the derived category of chain complexes. The first part of the thesis describes this surgery formula whose statement and proof are inspired by the Atiyah-Floer conjectures. The second part then contrasts with the Heegaard Floer analogue by showing that instanton and Heegaard Floer theory cannot agree over integers.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
In Copyright - Educational Use Permitted
Copyright retained by author(s)
Persistent DSpace Link
