2017/07/31 by Gavin Brown, Michael Wemyss · 12 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic number #Algebraic structure #Contraction (grammar) #FLOPS #Geometric and Algebraic Topology #Invariant (physics) #Rings, Modules, and Algebras #hep-th #math.AG
paper · pdf · doi:10.1007/s00220-017-3038-z
published in Communications in Mathematical Physics 361(1), 143-154 (Springer Science+Business Media) · 10 pages, final version
openalex created_date 2017/07/14 · arxiv created 2017/10/02 · openalex publication_date 2017/11/16 · arxiv updated 2017/12/06 · openalex updated_date 2026/08/05
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 D 4-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.