The blowup formula for higher rank Donaldson invariants

• Main Author: Culler, Lucas Howard
• Other Authors: Tomasz Mrowka.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2014
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/90181

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. === 16 === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 73-74). === 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. === by Lucas Howard Culler. === Ph. D.