In this paper, we define the notions of orbifold loop and orbifold road, with which, we reformulate the definition of orbifold fundamental group and deck translation group. We show that, for each orbifold, the orbifol...In this paper, we define the notions of orbifold loop and orbifold road, with which, we reformulate the definition of orbifold fundamental group and deck translation group. We show that, for each orbifold, the orbifold fundamental group is isomorphic to the deck translation group.展开更多
In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion f...In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion formula for Hurwitz-Hodge integral （TbL λgλ1）ag.展开更多
In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the pr...In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.展开更多
Let V be a vertex operator superalgebra and g=(12···k)be a k-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra V^(■k).In this paper,we construct an explicit is...Let V be a vertex operator superalgebra and g=(12···k)be a k-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra V^(■k).In this paper,we construct an explicit isomorphism from A_(g)(V^(■k))to A(V)if k is odd and to Aσ(V)if k is even whereσis the canonical automorphism of V of order 2 determined by the superspace structure of V.These recover previous results by Barron(2016)and Barron and Vander Werf(2014)that there is a one-to-one correspondence between irreducible g-twisted V^(■k)-modules and irreducible V-modules(resp.irreducibleσ-twisted V-modules)when k is odd(resp.even).This explicit isomorphism is expected to be useful in our further study on the Zhu algebra of the fixed point subalgebra.展开更多
We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line P[r].Furthermore,we deduce the explicit bilinear Fermionic formula for the(stationary...We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line P[r].Furthermore,we deduce the explicit bilinear Fermionic formula for the(stationary)Gromov-Witten potential via the lifting operator contructed from the Baker-Akhiezer function.展开更多
Comparing to the Ch-~Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifo...Comparing to the Ch-~Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods for almost complex orbifolds, we define the obstruction bundle for any 3-multisector of the almost contact orbifolds and the Chen^Ruan cup product for the Che-Ruan cohomology. We also prove that under this cup product the direct sum of all dimensional orbifold cohomology groups constitutes a cohomological ring. Finally we calculate two examples.展开更多
Comparing to the construction of stringy cohomology ring of equivariant sta-ble almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds,the authors constru...Comparing to the construction of stringy cohomology ring of equivariant sta-ble almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds,the authors construct in this note a Chen-Ruan cohomology ring for a stable almost complex orbifold.The authors show that for a finite group G and a G-equivariant stable almost complex manifold X,the G-invariant part of the stringy cohomology ring of(X,G)is isomorphic to the Chen-Ruan cohomology ring of the global quotient stable almost complex orbifold[X/G].Similar result holds when G is a torus and the action is locally free.Moreover,for a compact presentable stable almost complex orbifold,they study the stringy orbifold K-theory and its relation with Chen-Ruan cohomology ring.展开更多
In this paper,we consider double ramification cycles with orbifold targets.An explicit formula for double ramification cycles with orbifold targets,which is parallel to and generalizes the one known for the smooth cas...In this paper,we consider double ramification cycles with orbifold targets.An explicit formula for double ramification cycles with orbifold targets,which is parallel to and generalizes the one known for the smooth case,is provided.Some applications for orbifold Gromov–Witten theory are also included.展开更多
In this paper, one considers the change of orbifold Gromov Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of sym- pleetic orbifolds is proved. These result...In this paper, one considers the change of orbifold Gromov Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of sym- pleetic orbifolds is proved. These results extend the results of manifolds case to orbifold case.展开更多
In this paper,we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.
基金Supported by General Project of Science Research of Guangzhou(Grant No.2017070126)National Natural Science Foundation of China(Grant No.11226034).
文摘In this paper, we define the notions of orbifold loop and orbifold road, with which, we reformulate the definition of orbifold fundamental group and deck translation group. We show that, for each orbifold, the orbifold fundamental group is isomorphic to the deck translation group.
文摘In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion formula for Hurwitz-Hodge integral （TbL λgλ1）ag.
基金Supported by the Natural Science Foundation of China under Grant Nos. 10575080, 11047025, 11075126 the Project of Knowledge Innovation Program (PKIP) of Chinese Academy of Sciences
文摘In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.
基金supported by National Natural Science Foundation of China(Grant Nos.11971396,12131018 and 12161141001).
文摘Let V be a vertex operator superalgebra and g=(12···k)be a k-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra V^(■k).In this paper,we construct an explicit isomorphism from A_(g)(V^(■k))to A(V)if k is odd and to Aσ(V)if k is even whereσis the canonical automorphism of V of order 2 determined by the superspace structure of V.These recover previous results by Barron(2016)and Barron and Vander Werf(2014)that there is a one-to-one correspondence between irreducible g-twisted V^(■k)-modules and irreducible V-modules(resp.irreducibleσ-twisted V-modules)when k is odd(resp.even).This explicit isomorphism is expected to be useful in our further study on the Zhu algebra of the fixed point subalgebra.
基金Supported by National Key R&DProgram of China(Grant No.2020YFE0204200)NSFC(Grant Nos.12225101,12061131014 and 11890660)。
文摘We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line P[r].Furthermore,we deduce the explicit bilinear Fermionic formula for the(stationary)Gromov-Witten potential via the lifting operator contructed from the Baker-Akhiezer function.
基金supported in part by NSFC Project 60603004, 10631060
文摘Comparing to the Ch-~Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods for almost complex orbifolds, we define the obstruction bundle for any 3-multisector of the almost contact orbifolds and the Chen^Ruan cup product for the Che-Ruan cohomology. We also prove that under this cup product the direct sum of all dimensional orbifold cohomology groups constitutes a cohomological ring. Finally we calculate two examples.
基金supported by the National Natural Science Foundation of China(Nos.11501393,11626050,11901069)Sichuan Science and Technology Program(No.2019YJ0509)+1 种基金joint research project of Laurent Mathematics Research Center of Sichuan Normal University and V.C.&V.R.Key Lab of Sichuan Province,by Science and Technology Research Program of Chongqing Education Commission of China(No.KJ1600324)Natural Science Foundation of Chongqing,China(No.cstc2018jcyjAX0465).
文摘Comparing to the construction of stringy cohomology ring of equivariant sta-ble almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds,the authors construct in this note a Chen-Ruan cohomology ring for a stable almost complex orbifold.The authors show that for a finite group G and a G-equivariant stable almost complex manifold X,the G-invariant part of the stringy cohomology ring of(X,G)is isomorphic to the Chen-Ruan cohomology ring of the global quotient stable almost complex orbifold[X/G].Similar result holds when G is a torus and the action is locally free.Moreover,for a compact presentable stable almost complex orbifold,they study the stringy orbifold K-theory and its relation with Chen-Ruan cohomology ring.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11890663,12071322,11890660,11826102)the National Key R&D Program of China(Grant No.2020YFA0714000)+1 种基金the Sichuan Science and Technology Program(Grant Nos.2019YJ0509 and 2022JDTD0019)a joint research project of Laurent Mathematics Research Center of Sichuan Normal University and V.C.&V.R.Key Lab of Sichuan Province。
文摘In this paper,we consider double ramification cycles with orbifold targets.An explicit formula for double ramification cycles with orbifold targets,which is parallel to and generalizes the one known for the smooth case,is provided.Some applications for orbifold Gromov–Witten theory are also included.
基金partially supported by NSFC(Grant Nos.11228101,11371381)
文摘In this paper, one considers the change of orbifold Gromov Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of sym- pleetic orbifolds is proved. These results extend the results of manifolds case to orbifold case.
基金the National Natural Science Foundation of China(Grant No.10631060)the National Science Foundation and Hong Kong Research Grant Council Earmarked
文摘In this paper,we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.
