The blowup formula for higher rank Donaldson invariants
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2014
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| Online Access: | http://hdl.handle.net/1721.1/90181 |
| _version_ | 1811072991191105536 |
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| author | Culler, Lucas Howard |
| author2 | Tomasz Mrowka. |
| author_facet | Tomasz Mrowka. Culler, Lucas Howard |
| author_sort | Culler, Lucas Howard |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. |
| first_indexed | 2024-09-23T09:25:15Z |
| format | Thesis |
| id | mit-1721.1/90181 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T09:25:15Z |
| publishDate | 2014 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/901812019-04-11T13:10:23Z The blowup formula for higher rank Donaldson invariants Culler, Lucas Howard Tomasz Mrowka. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. 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. 2014-09-19T21:44:35Z 2014-09-19T21:44:35Z 2014 2014 Thesis http://hdl.handle.net/1721.1/90181 890210819 eng 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 74 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Culler, Lucas Howard The blowup formula for higher rank Donaldson invariants |
| title | The blowup formula for higher rank Donaldson invariants |
| title_full | The blowup formula for higher rank Donaldson invariants |
| title_fullStr | The blowup formula for higher rank Donaldson invariants |
| title_full_unstemmed | The blowup formula for higher rank Donaldson invariants |
| title_short | The blowup formula for higher rank Donaldson invariants |
| title_sort | blowup formula for higher rank donaldson invariants |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/90181 |
| work_keys_str_mv | AT cullerlucashoward theblowupformulaforhigherrankdonaldsoninvariants AT cullerlucashoward blowupformulaforhigherrankdonaldsoninvariants |