Automorphismes réels d'un fibré et opérateurs de Cauchy-Riemann

2011/10/31 by Rémi Crétois, Crétois, Rémi
Mathematics · #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.1110.6899

arxiv created 2011/10/31 · arxiv updated 2011/11/01

Abstract

Let (N,c_N) be a complex vector bundle equipped with a real structure over a real curve (Σ,c_Σ) of genus g ≥ 0. We compute the sign of the action of the automorphisms of (N,c_N) lifting the identity of Σ on the orientations of the determinant line bundle over the space of real Cauchy-Riemann operators on (N,c_N). This sign can be obtained as the product of two terms. The first one computes the signature of the permutations induced by the automorphisms acting on the Pin^± structures of the real part of (N,c_N). The second one comes from the action of the automorphisms of (N,c_N) on the bordism classes of real Spin structures on (Σ,c_Σ).

Related

• Real bundle automorphisms, Cauchy Riemann operators and orientability of moduli spaces
• Déterminant des opérateurs de Cauchy-Riemann réels et application à l'orientabilité d'espaces de modules de courbes réelles
• Automorphisms of moduli spaces of vector bundles over a curve
• The automorphism group of the moduli space of semi stable vector bundles
• Invariant Spin Structures on Riemann Surfaces