Volume 13, issue 1 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A mathematical theory of the topological vertex

Jun Li, Chiu-Chu Melissa Liu, Kefeng Liu and Jian Zhou

Geometry & Topology 13 (2009) 527–621
Abstract

We have developed a mathematical theory of the topological vertex—a theory that was originally proposed by M Aganagic, A Klemm, M Mariño and C Vafa on effectively computing Gromov–Witten invariants of smooth toric Calabi–Yau threefolds derived from duality between open string theory of smooth Calabi–Yau threefolds and Chern–Simons theory on three-manifolds.

Keywords
topological vertex, Gromov–Witten invariant, Calabi–Yau threefold
Mathematical Subject Classification 2000
Primary: 14N35, 53D45
Secondary: 57M27
References
Publication
Received: 23 October 2007
Revised: 27 July 2008
Accepted: 3 October 2008
Preview posted: 12 November 2008
Published: 1 January 2009
Proposed: Jim Bryan
Seconded: Lothar Goettsche, Eleny Ionel
Authors
Jun Li
Department of Mathematics
Stanford University
Stanford, CA 94305
USA
Chiu-Chu Melissa Liu
Department of Mathematics
Columbia University
New York, NY 10027
USA
Kefeng Liu
Center of Mathematical Sciences
Zhejiang University
Hangzhou 310027
China
and Department of Mathematics
University of California at Los Angeles
Los Angeles, CA 90095-1555
USA
Jian Zhou
Department of Mathematical Sciences
Tsinghua University
Beijing 100084
China