Profile
Profile

Prof. Dr. Carl-Friedrich Bödigheimer

E-mail: boedigheimer(at)math.uni-bonn.de
Phone: +49 228 73 7794
Fax: +49 228 73 62249
Homepage: http://www.math.uni-bonn.de/people/cfb/
Room: 4.013
Location: Mathematics Center
Institute: Bonn International Graduate School - BIGS
Mathematical Institute
Research Areas: Research Area F*
Research Area C (until 10/2012)
Former Research Area E
Date of birth: 12.Oct 1956

Academic Career

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 Profile

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 g=3 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.

Research Projects and Activities

Bonn International Graduate School in Mathematics
Director, 2001 - 2008

DFG Research Training Group GRK 1150 “Homotopy and Cohomology”
Coordinator, 2005 - 2008 and 2009 - 2014

Contribution to Research Areas

Research Area F*
The main achievement was the calculation of the homology and cohomology groups of the moduli space M_g,_1 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 Dyer-Lashof 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.

Selected Publications

[1] C.-F. Bödigheimer
Configuration models for moduli spaces of Riemann surfaces with boundary
Abh. Math. Sem. Univ. Hamburg , 76: : 191--233
2006
[2] Jochen Abhau, Carl-Friedrich Bödigheimer, Ralf Ehrenfried
Homology of the mapping class group Γ2,1 for surfaces of genus 2 with a boundary curve
The Zieschang Gedenkschrift
of Geom. Topol. Monogr. : 1--25
Publisher: Geom. Topol. Publ., Coventry
2008
[3] Carl-Friedrich Bödigheimer, Ulrike Tillmann
Stripping and splitting decorated mapping class groups
Cohomological methods in homotopy theory (Bellaterra, 1998)
of Progr. Math. : 47--57
Publisher: Birkhäuser, Basel
2001
[4] C.-F. Bödigheimer, F. R. Cohen, M. D. Peim
Mapping class groups and function spaces
Homotopy methods in algebraic topology (Boulder, CO, 1999)
of Contemp. Math. : 17--39
Publisher: Amer. Math. Soc., Providence, RI
2001
[5] C.-F. Bödigheimer, F. R. Cohen, R. J. Milgram
Truncated symmetric products and configuration spaces
Math. Z. , 214: (2): 179--216
1993
[6] C.-F. Bödigheimer, F. Cohen, L. Taylor
On the homology of configuration spaces
Topology , 28: (1): 111--123
1989
[7] C.-F. Bödigheimer, I. Madsen
Homotopy quotients of mapping spaces and their stable splitting
Quart. J. Math. Oxford Ser. (2) , 39: (156): 401--409
1988
[8] C.-F. Bödigheimer
Stable splittings of mapping spaces
Algebraic topology (Seattle, Wash., 1985)
of Lecture Notes in Math. : 174--187
Publisher: Springer, Berlin
1987
[9] C.-F. Bödigheimer
Splitting the Künneth sequence in K-theory. II
Math. Ann. , 251: (3): 249--252
1980
[10] Carl-Friedrich Bödigheimer
Splitting the Künneth sequence in K-theory
Math. Ann. , 242: (2): 159--171
1979

Publication List

MathSciNet Publication List (external link)

Habilitations

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

Selected PhD students

Michael Eisermann (2000): “Knotengruppen-Darstellungen und Invarianten von endlichem Typ”,
now Professor, University of Stuttgart

Birgit Richter (2000): “Taylorapproximationen und kubische Konstruktionen von Gamma-Moduln”,
now Professor, University of Hamburg

Johannes Ebert (2006): “Characteristic Classes of Spin Surface Bundles: Applications of the Madsen-Weiss 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

Supervised Theses

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