Journal article

### Floer theory for negative line bundles via Gromov-Witten invariants

Abstract:

We prove that the GW theory of negative line bundles M = Tot(L→B) determines the symplectic cohomology: indeed SH *(M) is the quotient of QH *(M) by the kernel of a power of quantum cup product by c1(L). We prove this also for negative vector bundles and the top Chern class. We calculate SH * and QH * for O(-n)→CPm. For example: for O(-1), M is the blow-up of Cm+1 at the origin and SH *(M) has rank m. We prove Kodaira vanishing: for very negative L, SH * = 0; and Serre vanishing: if we twist ...

### Access Document

Publisher copy:
10.1016/j.aim.2014.06.009

### Authors

Publisher:
Journal:
Volume:
262
Pages:
1035-1106
Publication date:
2014-09-10
DOI:
EISSN:
1090-2082
ISSN:
0001-8708
Source identifiers:
369649
Language:
English
Keywords:
Pubs id:
pubs:369649
UUID:
uuid:ece26f01-ae15-45c6-81de-9317985d7cc7
Local pid:
pubs:369649
Deposit date:
2014-07-27