Brown, G. and Wemyss, M. (2018) Gopakumar--Vafa invariants do not determine flops. Communications in Mathematical Physics, 361(1), pp. 143-154. (doi: 10.1007/s00220-017-3038-z)
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Abstract
Two 3-fold flops are exhibited, both of which have precisely one flopping curve. One of the two flops is new and is distinct from all known algebraic D4-flops. It is shown that the two flops are neither algebraically nor analytically isomorphic, yet their curve-counting Gopakumar–Vafa invariants are the same. We further show that the contraction algebras associated to both are not isomorphic, so the flops are distinguished at this level. This shows that the contraction algebra is a finer invariant than various curve-counting theories, and it also provides more evidence for the proposed analytic classification of 3-fold flops via contraction algebras.
| Item Type: | Articles |
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| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Wemyss, Professor Michael |
| Authors: | Brown, G., and Wemyss, M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Communications in Mathematical Physics |
| Publisher: | Springer |
| ISSN: | 0010-3616 |
| ISSN (Online): | 1432-0916 |
| Published Online: | 16 November 2017 |
| Copyright Holders: | Copyright © 2017 The Authors |
| First Published: | First published in Communications in Mathematical Physics 361(1):143-154 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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