2026-09-20T15:26:39Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/901812026-06-16T18:53:31Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Tomasz Mrowka.
Culler, Lucas Howard
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2014-09-19T21:44:35Z
2014-09-19T21:44:35Z
2014
2014
http://hdl.handle.net/1721.1/90181
890210819
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.
74 pages
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
The blowup formula for higher rank Donaldson invariants
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="26ea2925-4169-4c6b-996c-035ee438d172">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>The blowup formula for higher rank Donaldson invariants</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2014</PublicationDate>
<Authors>
<Author>
<DisplayName>Culler, Lucas Howard</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>