A compact topological surface S, possibly non-orientable and with non-empty boundary, always admits a Klein surface structure (an atlas whose transition maps are dianalytic). Its complex cover is, by definition, a compact Riemann surface X endowed with an antiholomorphic involution which determines topologically the original surface S. In this talk, we relate dianalytic vector bundles over S and holomorphic vector bundles over X, devoting special attention to the implications this has for moduli spaces of semistable bundles over X. We construct, starting from S, Lagrangian submanifolds of moduli spaces of semistable bundles of fixed rank and degree over X. This relates the present work to constructions of Ho and Liu over non-orientable compact surfaces with empty boundary.

© MPI f. Mathematik, Bonn | Impressum & Datenschutz |