In this paper we prove that for Gromov-Witten theory of orbifolds of ADE type the genus-2 G-function introduced by B. Dubrovin, S. Liu, and Y. Zhang vanishes. Together with our results in [LW], this completely solves the main conjecture in their paper [DLZ]. In the process, we also found a sufficient condition fo…
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11 results for “S^1-orbifold”
The paper classifies fibrations of 3-dimensional flat orbifolds.
problem Classifying fibrations of compact flat 3-orbifolds.
method Developed a theory for classifying fibrations of compact flat -orbifolds, applying it to 3-orbifolds.
result All geometric fibrations of compact, connected, flat 3-orbifolds, over a 1-orbifold, up to affine equivalence.
This paper classifies fibrations of flat orbifolds, advancing flat 4-manifold classification.
problem Classifying fibrations of compact flat orbifolds.
method Developed theory for classifying fibrations up to affine equivalence.
result Classified fibrations of compact flat 2-orbifolds.
For X = R, C, or H it is well known that cusp cross-sections of finite volume X-hyperbolic (n+1)-orbifolds are flat n-orbifolds or almost flat orbifolds modelled on the (2n+1)-dimensional Heisenberg group N_{2n+1} or the (4n+3)-dimensional quaternionic Heisenberg group N_{4n+3}(H). We give a necessary and sufficient co…
In this paper we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a 1-orbifold.
We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic (n+1)-orbifold.
The study finds a limit on subgroup complexity in hyperbolic 3-manifold groups.
problem Understanding subgroups of bounded rank in hyperbolic 3-manifold groups.
method Proving a finiteness theorem for subgroups of bounded rank.
result Every bounded rank covering tower of closed hyperbolic 3-manifolds is a tower of finite covers associated to a fibration over a 1-orbifold.
Study shows dynamics of rank 1 orbifolds in flat surfaces.
problem Characterize dynamics of rank 1 affine invariant orbifolds.
method Analyzes M-isoperiodic foliations and their ergodic properties.
result Leaves of the isoperiodic foliation are either all closed or all dense.
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat -manifold , we show that the set of similarity classes of flat metrics on which occur as a cusp cross-section of a hyperbolic -orbifold is dense in the space of similarity classes of flat metri…
Let G be an n-dimensional crystallographic group (n-space group). If G is a Z-reducible, then the flat n-orbifold E^n/G has a nontrivial fibered orbifold structure. We prove that this structure can be described by a generalized Calabi construction, that is, E^n/G is represented as the quotient of the Cartesian product …
The paper studies Sasaki-Ricci solitons on Sasakian manifolds up to seven dimensions.
problem Characterizing Sasaki-Ricci solitons on Sasakian manifolds of up to seven dimensions.
method Analysis of the Sasaki-Ricci flow and convergence to solitons.
result Existence and classification of Sasaki-Ricci solitons on Sasakian manifolds up to seven dimensions.