The purpose of this note is to study the three manifold invariants Qp(ML).For lens spaces L(7,1)and (7,2),we compute Q5(L(7,1) and Q5(L(7.2)) concretely,which enables us to prove that the in-variants can distinguish h...The purpose of this note is to study the three manifold invariants Qp(ML).For lens spaces L(7,1)and (7,2),we compute Q5(L(7,1) and Q5(L(7.2)) concretely,which enables us to prove that the in-variants can distinguish homotopy equivalence manifolds.展开更多
In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
We study the local Gromov-Witten invariants of O（k）⊕O（-k-2） → P1 by localization techniques and the Marino-Vafa formula, using suitable circle actions. They are identified with the equivariant Riemann-Roch indic...We study the local Gromov-Witten invariants of O（k）⊕O（-k-2） → P1 by localization techniques and the Marino-Vafa formula, using suitable circle actions. They are identified with the equivariant Riemann-Roch indices of some power of the determinant of the tautological sheaves on the Hilbert schemes of points on the affine plane. We also compute the corresponding Gopakumar-Vafa invariants and make some conjectures about them.展开更多
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conject...We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol'nyi-Prasad-Sommerfield(BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande.展开更多
We give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying relations in the tautological ring of the moduli space of2-pointed g...We give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying relations in the tautological ring of the moduli space of2-pointed genus-3 stable curves. A byproduct of our search for genus-3 equations is a new genus-2 universal equation for Gromov-Witten invariants.展开更多
The mixed spin P-fields （MSP for short） theory sets up a geometric platform to relate Gromov-Witten invariants of the quintic three-fold and Fan-Jarvis-Ruan-Witten invariants of the quintic polynomial in five variab...The mixed spin P-fields （MSP for short） theory sets up a geometric platform to relate Gromov-Witten invariants of the quintic three-fold and Fan-Jarvis-Ruan-Witten invariants of the quintic polynomial in five variables. It starts with Wittens vision and the P-fields treatment of GW invariants and FJRW invaxiants. Then it briefly discusses the master space technique and its application to the set-up of the MSP moduli. Some key results in MSP theory are explained and some examples are provided.展开更多
文摘The purpose of this note is to study the three manifold invariants Qp(ML).For lens spaces L(7,1)and (7,2),we compute Q5(L(7,1) and Q5(L(7.2)) concretely,which enables us to prove that the in-variants can distinguish homotopy equivalence manifolds.
文摘In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
基金supported by National Natural Science Foundation of China (Grant Nos.10425101,10631050)National Basic Research Program of China (973 Project) (Grant No. 2006cB805905)
文摘We study the local Gromov-Witten invariants of O（k）⊕O（-k-2） → P1 by localization techniques and the Marino-Vafa formula, using suitable circle actions. They are identified with the equivariant Riemann-Roch indices of some power of the determinant of the tautological sheaves on the Hilbert schemes of points on the affine plane. We also compute the corresponding Gopakumar-Vafa invariants and make some conjectures about them.
文摘We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol'nyi-Prasad-Sommerfield(BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande.
基金supported by National Security Agency(Grant No.H98230-10-1-0179)the National Science Foundation of USA(Grant No.DMS-0905227)+2 种基金a Tian-Yuan Special Fund of National Natural Science Foundation of China(Grant No.11326023)Specialized Research Fund for the Doctoral Program of Ministry of Higher Education(Grant No.20120001110051)Peking University 985 Fund
文摘We give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying relations in the tautological ring of the moduli space of2-pointed genus-3 stable curves. A byproduct of our search for genus-3 equations is a new genus-2 universal equation for Gromov-Witten invariants.
基金supported by Hong Kong General Research Fund(Nos.600711,6301515,602512)the National Science Foundation(Nos.NSF-1104553,DMS-1159156,DMS-1206667,DMS-1159416)
文摘The mixed spin P-fields （MSP for short） theory sets up a geometric platform to relate Gromov-Witten invariants of the quintic three-fold and Fan-Jarvis-Ruan-Witten invariants of the quintic polynomial in five variables. It starts with Wittens vision and the P-fields treatment of GW invariants and FJRW invaxiants. Then it briefly discusses the master space technique and its application to the set-up of the MSP moduli. Some key results in MSP theory are explained and some examples are provided.
