arXiv subjects

Georgios D. Daskalopoulos

Publications and source records attributed to Georgios D. Daskalopoulos.

3 recordsLinked to original sources

arXiv2010

Cohomology of SL(2,C) character varieties of surface groups and the action of the Torelli group

We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2,C) connections on a closed Riemann surface. We show that the trivial part of the action contains the equivariant cohomology of the even component of the space of flat PSL(2,C) connections. The non-trivial part consists of the even alternating products of degree two Prym representations, so that the kernel of the action is precisely the Prym-Torelli group. We compute the Betti numbers of the ordinary cohomology of the moduli space of flat SL(2,C) connections. Using results of Cappell-Lee-Miller we show that the Prym-Torelli group, which acts trivially on equivariant cohomology, acts non-trivially on ordinary cohomology.

math.GT↗

arXiv2006

Harmonic Maps and Teichmueller Theory

This is a survey article to appear in the "Handbook on Teichmueller Theory".

math.CV↗

arXiv2004

Convergence properties of the Yang-Mills flow on Kaehler surfaces

Let $E$ be a hermitian complex vector bundle over a compact Kähler surface $X$ with Kähler form $ω$, and let $D$ be an integrable unitary connection on $E$ defining a holomorphic structure $D^{\prime\prime}$ on $E$. We prove that the Yang-Mills flow on $(X,ω)$ with initial condition $D$ converges, in an appropriate sense which takes into account bubbling phenomena, to the double dual of the graded sheaf associated to the $ω$-Harder-Narasimhan-Seshadri filtration of the holomorphic bundle $(E,D^{\prime\prime})$. This generalizes to Kähler surfaces the known result on Riemann surfaces and proves, in this case, a conjecture of Bando and Siu.

math.DG↗