Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds

Li, An Min; Ruan, Yongbin

doi:10.1007/s002220100146

Cited by 319 publications

(462 citation statements)

References 32 publications

Supporting

Mentioning

453

Contrasting

Order By: Relevance

“…The gluing here is analytically closely related to gluing problems which arose in the study of the Yang-Mills equations (see for example [36], [24]). Moreover, the degeneration of Σ above is closely related to the degenerations studied by Ionel-Parker and Li-Ruan which concern degenerations of symplectic manifolds along codimension one symplectic submanifolds (see [18], [20]). The rest of this section is devoted to proving Theorem 10.2.…”

Section: Sketch Of Proofmentioning

confidence: 87%

Holomorphic disks and topological invariants for closed three-manifolds

2004

View full text Add to dashboard Cite

show abstract

Section: Sketch Of Proofmentioning

confidence: 87%

Holomorphic disks and topological invariants for closed three-manifolds

2004

View full text Add to dashboard Cite

show abstract

“…The construction of relative stable maps was first developed in the symplectic category [LR,IP1,IP2]. Recently in [Lil,Li2] the first author of the present paper has given an algebro-geometric definition of the moduli space of relative stable morphisms and has constructed relative Gromov-Witten invariants in the algebraic category.…”

Section: Jliandys Songmentioning

confidence: 99%

Open string instantons and relative stable morphisms

Li¹,

Song²

2001

Advances in Theoretical and Mathematical Physics

View full text Add to dashboard Cite

We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics. By using the method of virtual localization, we successfully reproduce their results for multiple covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold of a Calabi-Yau 3-fold, by Riemann surfaces with arbitrary genera and number of boundary components. In particular we show that, in the case we consider, there are no open string instantons with more than one boundary component ending on the Lagrangian submanifold. e-print archive: http://xxx.laiil.gov/abs/hep-th/0103100

show abstract

“…The theory of relative stable maps ( [LR01], [Li02]) extends this scenario to more general Hurwitz numbers, with arbitrary ramification profiles over the branch points.…”

Section: Introductionmentioning

confidence: 96%

Tropical Hurwitz Numbers

Cavalieri

Johnson

Markwig

2016

Riemann Surfaces and Algebraic Curves

View full text Add to dashboard Cite

Abstract. Hurwitz numbers count genus g, degree d covers of P 1 with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piece-wise linear objects called tropical curves. This paper develops a tropical counterpart of the branch map and shows that its degree recovers classical Hurwitz numbers.

show abstract

Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds

Cited by 319 publications

References 32 publications

Holomorphic disks and topological invariants for closed three-manifolds

Holomorphic disks and topological invariants for closed three-manifolds

Open string instantons and relative stable morphisms

Tropical Hurwitz Numbers

Contact Info

Product

Resources

About