Prof. Dr. (em.) Matthias Kreck

E-Mail: kreck(at)
Telefon: +49 228 73 7785
Raum: 3.007
Standort: Mathematics Center
Institute: Mathematical Institute
Forschungsbereiche: Research Area A
Research Area F*
Former Research Area F
Geburtsdatum: 22.Jul 1947
Mathscinet-Number: 106415

Academic Career

1970 - 1976

Assistant of F. Hirzebruch, University of Bonn


Dissertation, University of Bonn (advisor: F. Hirzebruch)


Professor (H3), University of Wuppertal


Habilitation, University of Bonn


Professor (C4), University of Mainz

1994 - 2002

Director, Oberwolfach Research Institute for Mathematics (MFO)


Professor (C4), University of Heidelberg

2007 - 2011

Director, Hausdorff Research Institute for Mathematics, University of Bonn

2007 - 2014

Professor, University of Bonn

Since 2014

Professor Emeritus

Contribution to Research Areas

Research Area A
I am interested in stratifolds, a generalization of manifolds which I introduced. These are differential topological objects and so (besides topological applications) one can try to prove analytical statements for stratifolds. In this direction I studied de Rham cohomology for stratifolds [1], [2].
Another related research concerns the construction of quantum field theories [3].
Former Research Area F
Following Felix Klein almost all mathematics can be formulated in terms of group actions. My main contributions concern asymmetric manifolds, classification of 4-manifolds with fundamental group Baumslag/Solitar and construction of equivariant cohomology theories [4], [5], [6], [7].

Selected Publications

[1] Ulrich Bunke, Matthias Kreck, Thomas Schick
A geometric description of differential cohomology
Ann. Math. Blaise Pascal , 17: (1): 1--16
[2] Matthias Kreck
Differential algebraic topology
From stratifolds to exotic spheres
of Graduate Studies in Mathematics : xii+218
Publisher: American Mathematical Society, Providence, RI
ISBN: 978-0-8218-4898-2
DOI: 10.1090/gsm/110
[3] Henning Hohnhold, Matthias Kreck, Stephan Stolz, Peter Teichner
Differential forms and 0-dimensional supersymmetric field theories
Quantum Topol. , 2: (1): 1--41
DOI: 10.4171/QT/12
[4] Ian Hambleton, Matthias Kreck, Peter Teichner
Topological 4-manifolds with geometrically two-dimensional fundamental groups
J. Topol. Anal. , 1: (2): 123--151
DOI: 10.1142/S1793525309000084
[5] M. Kreck, W. Lück
Topological rigidity for non-aspherical manifolds
Pure Appl. Math. Q. , 5: (3, Special Issue: In honor of Friedrich Hirzebruch. Part 2): 873--914
DOI: 10.4310/PAMQ.2009.v5.n3.a1
[6] Matthias Kreck, Volker Puppe
Involutions on 3-manifolds and self-dual, binary codes
Homology Homotopy Appl. , 10: (2): 139--148
[7] Matthias Kreck, Peter Teichner
Positivity of topological field theories in dimension at least 5
J. Topol. , 1: (3): 663--670
DOI: 10.1112/jtopol/jtn016

Publication List


• Mathematische Annalen (1990 - 1998)
• Archiv der Mathematik (1998 - 2002)



Member of the Heidelberg Academy of Sciences and Humanities


Doctor honoris causa, University of Siegen


Cantor medal of the German Mathematical Society



University of Munich

Selected PhD students

Stephan Stolz (1983): “Untersuchung hochzusammenhängender Mannigfaltigkeiten und ihrer Ränder”,
now Professor, University of Notre Dame, IN, USA

Peter Teichner (1992): “Topological 4-manifolds with finite fundamental group”,
now Director of Max Planck Institute for Mathematics, Bonn

Stefan Bechtluft-Sachs (1993): “On the eta-Invariant of Dirac Operators on Manifolds with Free Circle Action”,
now Lecturer, Maynooth University, Ireland

Stephan Klaus (1995): “Brown-Kervaire Invariants”,
now Scientific Administrator, Oberwolfach Research Institute for Mathematics (MFO), and Professor (Apl), University of Mainz

Anand Dessai (1996): “Rigidity Theorums for Spin c-Manifolds”,
now Professor, University of Fribourg, Switzerland

Christian-Oliver Ewald (2002): “Hochschild Homology and De Rham Cohomology of Stratifolds”,
now Professor, Adam Smith Business School, University of Glasgow, Scotland, UK

Yang-Su (2007): “Singular Hypersurfaces as Stratifolds”,
now Associate Professor, Beijing, China

Supervised Theses

  • PhD theses: 20
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