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We present a formula for the full Cheeger-Chern-Simons class of the tautological flat complex vector bundle of rank 2 over BSL(2, C δ ). Our formula improves the formula in [DZ], where the c...
CUP PRODUCTS, THE HEISENBERG GROUP, AND CODIMENSION TWO ALGEBRAIC CYCLES     CUP PRODUCTS  HEISENBERG GROUP       font style='font-size:12px;'> 2015/12/10
We de ne higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This...
ACTION OF THE JOHNSON-TORELLI GROUP ON REPRESENTATION VARIETIES     JOHNSON-TORELLI  mapping class group       font style='font-size:12px;'> 2015/9/29
Let Σ be a compact orientable surface with genus g and n boundary components B = (B1,...,Bn). Let c = (c1,...,cn) ∈ [−2,2]n. Then the mapping class group MCG of Σ acts on the relative SU(2)-cha...
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)-...
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.
We pose some graph theoretic conjectures about duality and the diameter of maximal trees in planar graphs, and we describe innovations in the following two topics in Geometric Group Theory, where the ...
The Dehn function of Baumslag's metabelian group     Baumslag's metabelian group  Cm-wreath-Z       font style='font-size:12px;'> 2015/8/26
Baumslag's group is a finitely presented metabelian group with a Z–wreath–Z subgroup. There is an analogue with an additional torsion relation in which this subgroup becomes Cm–wreath–Z. We prove that...
It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R^2 into ...
Abstract: Given a positive and unitarily invariant Lagrangian L defined in the algebra of Hermitian matrices, and a fixed interval $[a,b]\subset\mathbb R$, we study the action defined in the Lie group...
The generalized wreath product of permutation groups is intro-duced. By means of it we study the schurity problem for S-rings over a cyclic group G and the automorphism groups of them.
In this paper, we give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with the action...
We use earlier results on the classification of the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). These results are applied to the reduct...
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...
Affine embeddings of a reductive group      Affine embeddings  reductive group        font style='font-size:12px;'> 2011/2/22
We classify affine varieties with an action of a connected,reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one...
Group Width     Group Width  Geometric Topology       font style='font-size:12px;'> 2010/11/18
There are many "minimax" complexity functions in mathematics: width of a tree or a link, Heegaard genus of a 3-manifold, the Cheeger constant of a Riemannian manifold. We define such a function w, "wi...

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