

1979  Diploma, University of Heidelberg  1980  MasterofScience, 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, JohnsHopkinsUniversity, 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 


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 little2cube 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 MumfordMillerMorita 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.


Bonn International Graduate School in Mathematics
Director, 2001  2008
DFG Research Training Group GRK 1150 “Homotopy and Cohomology”
Coordinator, 2005  2008 and 2009  2014


Research Area F* The main achievement was the calculation of the homology and cohomology groups of the moduli space of Riemann surfaces with one boundary curve in the cases g = 2 and g = 3. For genus 3 we could compute the groups; in genus 2 we can also describe generators of these groups in terms of homology operations such as DyerLashof operations. The methods used include models for moduli spaces and the calculation of homology operations as well as smaller chain models, based on discrete Morse theory and certain normal forms on symmetric groups and their bar resolution. 


[ 1] C.F. BÃ¶digheimer
Configuration models for moduli spaces of Riemann surfaces with boundary Abh. Math. Sem. Univ. Hamburg , 76: : 191233 2006 DOI: 10.1007/BF02960865[ 2] Jochen Abhau, CarlFriedrich BÃ¶digheimer, Ralf Ehrenfried
Homology of the mapping class group Î?_{2,1} for surfaces of genus 2 with a boundary curve The Zieschang Gedenkschrift of Geom. Topol. Monogr. : 125 Publisher: Geom. Topol. Publ., Coventry 2008 DOI: 10.2140/gtm.2008.14.1[ 3] CarlFriedrich BÃ¶digheimer, Ulrike Tillmann
Stripping and splitting decorated mapping class groups Cohomological methods in homotopy theory (Bellaterra, 1998) of Progr. Math. : 4757 Publisher: BirkhÃ¤user, Basel 2001[ 4] C.F. BÃ¶digheimer, F. R. Cohen, M. D. Peim
Mapping class groups and function spaces Homotopy methods in algebraic topology (Boulder, CO, 1999) of Contemp. Math. : 1739 Publisher: Amer. Math. Soc., Providence, RI 2001 DOI: 10.1090/conm/271/04348[ 5] C.F. BÃ¶digheimer, F. R. Cohen, R. J. Milgram
Truncated symmetric products and configuration spaces Math. Z. , 214: (2): 179216 1993 DOI: 10.1007/BF02572399[ 6] C.F. BÃ¶digheimer, F. Cohen, L. Taylor
On the homology of configuration spaces Topology , 28: (1): 111123 1989 DOI: 10.1016/00409383(89)900359[ 7] C.F. BÃ¶digheimer, I. Madsen
Homotopy quotients of mapping spaces and their stable splitting Quart. J. Math. Oxford Ser. (2) , 39: (156): 401409 1988 DOI: 10.1093/qmath/39.4.401[ 8] C.F. BÃ¶digheimer
Stable splittings of mapping spaces Algebraic topology (Seattle, Wash., 1985) of Lecture Notes in Math. : 174187 Publisher: Springer, Berlin 1987 DOI: 10.1007/BFb0078741[ 9] C.F. BÃ¶digheimer
Splitting the KÃ¼nneth sequence in Ktheory. II Math. Ann. , 251: (3): 249252 1980 DOI: 10.1007/BF01428944[ 10] CarlFriedrich BÃ¶digheimer
Splitting the KÃ¼nneth sequence in Ktheory Math. Ann. , 242: (2): 159171 1979 DOI: 10.1007/BF01420413





Ulrike Tillmann (1995), now Professor, University of Oxford, England, UK


Michael Eisermann (2000): “KnotengruppenDarstellungen und Invarianten von endlichem Typ”,
now Professor, University of Stuttgart
Birgit Richter (2000): “Taylorapproximationen und kubische Konstruktionen von GammaModuln”,
now Professor, University of Hamburg
Johannes Ebert (2006): “Characteristic Classes of Spin Surface Bundles: Applications of the MadsenWeiss Theory”,
now Professor, University of Münster
Viktoriya Ozornova (2012): “Factoribility, discrete Morse theory and a reformulation of the K(\pi,1)conjecture”,
now Assistant, University of Bochum


 Master theses: 6
 Diplom theses: 44
 PhD theses: 16, currently 2


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