Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant
Author Manuscript: 4 Apr 2011
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
International Press of Boston, Inc.
2013
|
| Online Access: | http://hdl.handle.net/1721.1/80399 https://orcid.org/0000-0001-9520-6535 |
| _version_ | 1826198395778236416 |
|---|---|
| author | Mrowka, Tomasz S. Ruberman, Daniel Saveliev, Nikolai |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Mrowka, Tomasz S. Ruberman, Daniel Saveliev, Nikolai |
| author_sort | Mrowka, Tomasz S. |
| collection | MIT |
| description | Author Manuscript: 4 Apr 2011 |
| first_indexed | 2024-09-23T11:04:12Z |
| format | Article |
| id | mit-1721.1/80399 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:04:12Z |
| publishDate | 2013 |
| publisher | International Press of Boston, Inc. |
| record_format | dspace |
| spelling | mit-1721.1/803992022-10-01T00:56:25Z Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant Mrowka, Tomasz S. Ruberman, Daniel Saveliev, Nikolai Massachusetts Institute of Technology. Department of Mathematics Mrowka, Tomasz S. Author Manuscript: 4 Apr 2011 We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold X with the homology of S[superscript 1]×S[superscript 3]. The invariant has two terms: one is a count of solutions to the Seiberg–Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with end modeled on the infinite cyclic cover of X. Each term is metric (and perturbation) dependent, and we show that these dependencies cancel as the metric and perturbation vary in a generic 1-parameter family. 2013-09-11T18:02:09Z 2013-09-11T18:02:09Z 2011-06 Article http://purl.org/eprint/type/JournalArticle 0022-040X 1945-743X http://hdl.handle.net/1721.1/80399 Mrowka, Tomasz et al. “Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant.” Journal of Differential Geometry 88 (2011): 333–377. https://orcid.org/0000-0001-9520-6535 en_US http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&page=toc&handle=euclid.jdg/1320067645 Journal of Differential Geometry Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf International Press of Boston, Inc. arXiv |
| spellingShingle | Mrowka, Tomasz S. Ruberman, Daniel Saveliev, Nikolai Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant |
| title | Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant |
| title_full | Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant |
| title_fullStr | Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant |
| title_full_unstemmed | Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant |
| title_short | Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant |
| title_sort | seiberg witten equations end periodic dirac operators and a lift of rohlin s invariant |
| url | http://hdl.handle.net/1721.1/80399 https://orcid.org/0000-0001-9520-6535 |
| work_keys_str_mv | AT mrowkatomaszs seibergwittenequationsendperiodicdiracoperatorsandaliftofrohlinsinvariant AT rubermandaniel seibergwittenequationsendperiodicdiracoperatorsandaliftofrohlinsinvariant AT savelievnikolai seibergwittenequationsendperiodicdiracoperatorsandaliftofrohlinsinvariant |