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THE EXTENDED BLOCH GROUP AND THE CHEEGER-CHERN-SIMONS CLASS
THE EXTENDED BLOCH GROUP CHEEGER-CHERN-SIMONS CLASS
2015/12/17
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
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
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
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.
Some duality conjectures for finite graphs and their group theoretic consequences
finite graphs group theoretic consequences
2015/8/26
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 ...
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...
Some properties of Holder surfaces in the Heisenberg group
properties of Holder surfaces Heisenberg group Differential Geometry
2012/5/9
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 ...
Optimal paths for symmetric actions in the unitary group
geodesic segment Lagrangian optimal path unitarily invariant norm unitary group Grassmann manifold angular metric
2011/9/5
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...
Schurity of S-rings over a cyclic group and generalized wreath product of permutation groups
Schurity of S-rings cyclic group generalized wreath product of permutation groups
2011/2/25
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.
The bounded spherical functions for the free two step nilpotent Lie group
nilpotent Lie group representation theory spherical function
2011/1/19
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...
Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry
Group-Theoretical Classification of BPS Possibly Protected States D=4 Conformal Supersymmetry
2011/3/3
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...
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...
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
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...