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ERGODICITY OF MAPPING CLASS GROUP ACTIONS ON SU(2)-CHARACTER VAR IET IES     GROUP ACTIONS  MAPPING CLASS       font style='font-size:12px;'> 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)-...
We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is ex...
For a countable group G and a standard Borel G-space X, a countable Borel partition P of X is called a generator if {gA : g in G, A in P} generates the Borel sigma-algebra of X. For G=Z, the Kolmogoro...
Abstract: We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\sigma \geq 2$ is at least quadratic in $\sigma$. We do this through the introduction of a co...
Resolution of smooth group actions      Resolution  smooth group actions        font style='font-size:12px;'> 2011/2/28
A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds ...
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary discrete series of the Virasoro algebra with 0 < c < 1. The proof showed directly that the mutliplicity sp...
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset diffeology of the functio...
Equivalence of Group Actions on Riemann Surfaces      Equivalence of Group  Riemann Surfaces        font style='font-size:12px;'> 2011/2/24
We produce for each natural number n  3 two 1–parameter fam-ilies of Riemann surfaces admitting automorphism groups with two cyclic sub-groups H1 and H2 of orden 2n, that are conjugate in the group o...
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
In his volume [5] on "Symmetry Breaking for Compact Lie Groups" Mike Field quotes a private communication by Jorge Ize claiming that any bifurcation problem with absolutely irreducible group action wo...
We construct holomorphic families of proper holomorphic embeddings of $\C^k$ into $\C^n$ ($0 so that for any two different parameters in the family no holomorphic automorphism of $\C^n$ can ...
If G is a finite ℓ-group acting on an affine space An over a finite field K of cardinality prime to ℓ, Serre [29] shows that there exists a rational fixed point. We generalize this to the ...
A Borsuk-Ulak Theorem for Heisenberg Group Actions     Borsuk-Ulam Type Theorem  Cohomological Index  Group Action       font style='font-size:12px;'> 2010/3/1
Let G=H2n+1 be a (2n+1)-dimensional Heisenberg Lie group acts on M=Cm-\{0\} and M'=Cm'-\{0\} exponentially. By using Cohomological Index we proved the following theorem. If f:M{\to}M' is a G-equivaria...
Braid group actions on derived categories of coherent sheaves     Braid group  derived categories  coherent sheaves       font style='font-size:12px;'> 2010/10/29
This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety $X$. The motivation for this is Kontsevich's homological mirror conjecture, together wit...

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