Surface Group Representations and U(p, q)-Higgs Bundles

Abstract

Members of VBAC (Vector Bundles on Algebraic Curves), which is partially supported by EAGER (EC FP5 Contract no. HPRN-CT-2000-00099) and by EDGE (EC FP5 Contract no. HPRN-CT-2000-00101). 2 Partially supported by the National Science Foundation under grant DMS-0072073 3 Partially supported by the Ministerio de Ciencia y Tecnología (Spain) under grant BFM2000-0024 4 Partially supported by the Fundação para a Ciência e a Tecnologia (Portugal) through the Centro de Matemática da Universidade do Porto and through grant no. SFRH/BPD/1606/2000.

Moduli of ADHM sheaves and the local Donaldson–Thomas theory

“…Analogous stability conditions for quiver sheaves were previously formulated and studied in [73,30,74], and in the context of HitchinKobayashi correspondence in [2,1]. This is a natural generalization of previous work on decorated sheaves, including [13,79,14,15,9,41,40,75].…”

A Measurable Cartan Theorem and Applications to Deformation Rigidity in Complex Hyperbolic Geometry

“…Let M := Γ\H p C be the finite volume quotient and assume that either p ≥ 2 or M is compact. Then the L 2 -cohomology space H 2 (2) (M ) injects into H 2 dR (M ) H 2 (Γ, R), and it is a fact that the pullback ρ (2) (κ q ), seen as an element of H 2 dR (M ), belongs to the subspace H 2 (2) (M ), see [3]. Since M is at any rate locally Hermitian symmetric, we may identify H k (2) (M ) with the space of harmonic k-forms which are L 2 on M ; in particular H 2 (2) (M ) comes with the natural inner product of L 2 -forms, and the Kähler form ω M coming from ω p defines then an element of H 2 (2) (M ).…”

Zwischen Flexibilität und Starrheit. Gruppenhomomorphismen und geometrische Strukturen

“…In den letzten Jahren wurden viele Fortschritte beim Verständnis von Homomorphismen von φ : Γ g → G erzielt, z. B. für G = SL(n, R), Sp(2n, R) oder SU(n, m) [9,10,8,11,7,2,3,4,12]. Dabei spielen auch Verallgemeinerungen der Eulerzahl und verallgemeinerte Doppelverhältnisse eine Rolle.…”