Saglam, Murat (2022). Holomorphic curves in the symplectizations of lens spaces: An elementary approach. Muenster J. Math., 15 (2). S. 389 - 441. MUENSTER: WESTFAELISCHE WILHELMS-UNIV MUENSTER, MATH INST. ISSN 1867-5786
Full text not available from this repository.Abstract
We present an elementary computational scheme for the moduli spaces of rational pseudo-holomorphic curves in the symplectizations of 3-dimensional lens spaces, which are equipped with Morse-Bott contact forms induced by the standard Morse-Bott contact form on S3. As an application, we prove that, for p prime and 1 < q, q ' <p - 1, if there is a contactomorphism between lens spaces L(p, q) and L(p, q '), where both spaces are equipped with their standard contact structures, then q = (q ')+/- 1 in mod p. For the proof, we study the moduli spaces of a pair of pants with two non-contractible ends in detail and establish that the standard almost complex structure that is used is regular. Then the existence of a contactomorphism enables us to follow a neck-stretching process, by means of which we compare the homotopy relations encoded at the non-contractible ends of the pair of pants in the symplectizations of L(p, q) and L(p, q '). Combining our proof with the result of Honda on the classification of universally tight contact structures on lens spaces, we provide a purely symplectic/contact topological proof of the diffeomorphism classification of lens spaces in the class mentioned above.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-659751 | ||||||||
| DOI: | 10.17879/21089689454 | ||||||||
| Journal or Publication Title: | Muenster J. Math. | ||||||||
| Volume: | 15 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | S. 389 - 441 | ||||||||
| Date: | 2022 | ||||||||
| Publisher: | WESTFAELISCHE WILHELMS-UNIV MUENSTER, MATH INST | ||||||||
| Place of Publication: | MUENSTER | ||||||||
| ISSN: | 1867-5786 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/65975 |
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