## The blowup formula for higher rank Donaldson invariants

##### Author(s)

Culler, Lucas Howard
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##### Other Contributors

Massachusetts Institute of Technology. Department of Mathematics.

##### Advisor

Tomasz Mrowka.

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Show full item record##### Abstract

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

2014##### Department

Massachusetts Institute of Technology. Department of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.