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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity results in mapping class groups and homeomorphism groups
映射类群 同胚群 刚性结果
2023/11/13
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
The 1st Asian Pacific Conference on Concept Mapping (CMC-AP 2017) will take place in Beijing, China from Sept 20-22, 2017.The theme for CMC-AP 2017 will be Learning for Understanding the World and Our...
The 1st Asian Pacific Conference on Concept Mapping
The 1st Asian Pacific Conference Concept Mapping
2017/7/4
The 1st Asian Pacific Conference on Concept Mapping (CMC-AP 2017) will take place in Beijing, China from Sept 20-22, 2017.The theme for CMC-AP 2017 will be Learning for Understanding the World and Our...
THE ACTION OF THE MAPPING CLASS GROUP ON REPRESENTATION VARIETIES
MAPPING CLASS GROUP REPRESENTATION VARIETIES
2015/12/17
These notes are based on lectures given at Zhejiang University, July 14–20, 2008. My goal was to present some analytic techniques that can be used to study the action of the mapping class group on the...
ERGODICITY OF MAPPING CLASS GROUP ACTIONS ON SU(2)-CHARACTER VAR IET IES
GROUP ACTIONS MAPPING CLASS
2015/9/29
Let be a compact orientable surface with genus g andnboundary components
∂1,..., ∂n. Let b = (b1,...,bn) ∈ [−2,2]
n. Then the mapping class group
Mod() acts on the relative SU(2)-...
THE MAPPING CLASS GROUP ACTS REDUCIBLY ON SU(n)-CHARACTER VARIETIES
CLASS GROUP ACTS REDUCIBLY VARIETIES
2015/9/29
When G is a connected compact Lie group, and π
is a closed surface group, then Hom(π, G)/G contains an open
dense Out(π)-invariant subset which is a smooth symplectic manifold.
SET MAPPING REFLECTION
MAPPING REFLECTION
2015/8/17
The goal of these lectures is to give an exposition of the concept of an open stationary set, an associated reflection principle (for lack of a better word), and a list of examples of how this sort of...
Given a homotopy equivalence f between two topological spaces we obtain an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.
Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifolds
Homological eigenvalues mapping classes torsion homology growth fibered 3--manifolds Group Theory
2012/5/9
Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on th...
On visualization of the linearity problem for mapping class groups of surfaces
visualization linearity problem mapping class groups surfaces
2012/3/1
We derive two types of linearity conditions for mapping class groups of orientable surfaces; one for once-punctured surface, and the other for closed surface, respectively. For the once-punctured case...
The Hessenberg matrix and the Riemann mapping
Hessenberg matrix Riemann mapping Spectral Theory
2011/9/29
Abstract: We show in this paper that, if \mu is a regular measure whose support is a Jordan arc or a connected finite union of Jordan arcs in the complex plane \mathbb{C}, then the limits of the eleme...
The Witten-Reshetikhin-Turaev invariants of finite order mapping tori II
The Witten-Reshetikhin-Turaev invariants finite order mapping tori II Geometric Topology
2011/8/31
Abstract: We identify the leading order term of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-c...
Conformal Mapping of Circular Quadrilaterals and Weierstrass Elliptic Functions
conformal mapping accessory parameter Schwarzian derivative
2011/2/21
Numerical and theoretical aspects of conformal mappings from a disk to a circular-arc quadrilateral, symmetric with respect to the coordinate axes, are devel-oped.
A faithful linear-categorical action of the mapping class group of a surface with boundary
faithful linear-categorical action mapping class group surface with boundary
2011/1/18
We show that the action of the mapping class group on bordered Floer homology in the second to extremal spinc-structure is faithful. The paper is self-contained, and in particular does not assume any ...
Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
$D_N$ type quantum Calogero model through free harmonic oscillators
2011/3/3
We solve the eigenvalue problem of the DN type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation.In particular, we construct the ei...