Prof. Dr. Carl-friedrich Bödigheimer

Biography

My research interests are centered around the moduli spaces of Riemann surfaces. The surfaces have always (a) at least one boundary curve, or (b) have their boundary curves partitioned into at least one incoming and at least one outgoing curve. These moduli spaces are manifolds and classifying spaces of the corresponding mapping class groups; in case (b) they are spaces of bordisms and are therefore important for string topology and topological field theories. We have developed the theses moduli spaces simplicial models (up to homeomorphism), built out of strata of classifying spaces of symmetric groups. Furthermore, there is an operad structure of the little-2-cube operads and a plentitude of further homology operations. Using these operations we could describe the integral homology and its generators in case (a) for genus 2.  In the future we want to extend this description of the integral homology and its generators for  and to the case (b). This should lead to connections with Sullivan diagrams used in string topology.  A second project is the description of the Mumford-Miller-Morita classes in the concrete models mentioned above.  A third project concerns the generalisation of such a description of the homology to moduli spaces of bundles over surfaces; so this, the symmetric groups need to be replaced by Coxeter groups. 1979 Diploma, University of Heidelberg 1980 Master-of-Science, Oxford University, England, UK 1982 - 1984 Graduate studies, University of Heidelberg 1984 PhD, University of Heidelberg 1984 - 1985 Postdoc, University of Göttingen 1985 - 1991 Assistant Professor (C1), University of Göttingen 1990 Habilitation, University of Göttingen 1991 - 1992 Visiting Assistant Professor, Johns-Hopkins-University, Baltimore, MD, USA 1992 - 1993 Heisenberg grant 1992 - 1993 Guest at Institute for Advanced Studies, Princeton University, NJ, USA Since 1993 Professor (C3), University of Bonn

Research Interest

Research Area F* Research Area C Former Research Area E