The blowup formula for higher rank Donaldson invariants
Author(s)
Culler, Lucas Howard![Thumbnail](/bitstream/handle/1721.1/90181/890210819-MIT.pdf.jpg?sequence=5&isAllowed=y)
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Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Tomasz Mrowka.
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In this thesis, I study the relationship between the higher rank Donaldson invariants of a smooth 4-manifold X and the invariants of its blowup X#CP2 . This relationship can be expressed in terms of a formal power series in several variables, called the blowup function. I compute the restriction of the blowup function to one of its variables, by solving a special system of ordinary differential equations. I also compute the SU(3) blowup function completely, and show that it is a theta function on a family of genus 2 hyperelliptic Jacobians. Finally, I give a formal argument to explain the appearance of Abelian varieties and theta functions in four dimensional topological field theories.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. 16 Cataloged from PDF version of thesis. Includes bibliographical references (pages 73-74).
Date issued
2014Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.