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Invariant functions on Lie groups and Hamiltonian flows ofsurface group representations
Lie groups Hamiltonian flows
2015/9/29
In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S
and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G
of conjugacy classes of representat...
The dead-end depth of an element g of a group G with generating set A is the distance from g to the complement of the radius d(1,g) closed ball, in the word metric d defined with respect to A. We exhi...
The paper was motivated by a question of Vilonen, and the main
results have been used by Mirkovi′c and Vilonen to give a geometric interpretation of the dual group (as a Chevalley group over Z) of a ...
A note on the unramified Brauer group of a homogeneous space
Unramified Brauer group homogeneous space linear algebraic group
2012/6/21
We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the un...
The Homotopy Sequence of Nori's Fundamental Group
The Homotopy Sequence of Nori's Fundamental Group Algebraic Geometry
2012/6/18
In this paper, we investigate the necessary sufficient conditions for the exactness of the homotopy sequence of Nori's fundamental group and apply these to various special situations to regain some cl...
A Lower Bound for the Number of Group Actions on a Compact Riemann Surface
Riemann surface automorphism signature mapping class group
2011/9/14
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...
The overarching finite symmetry group of Kummer surfaces in the Mathieu group M_24
Kummer surfaces Mathieu group High Energy Physics - Theory Algebraic Geometry
2011/10/9
Abstract: We construct a bijection between the full integral homology lattice of K3 and a Niemeier lattice, which is simultaneously compatible with the finite symplectic automorphism groups of several...