From minimal geodesics to super symmetric field theories. In memory of Raoul Bott.
Raoul Bott 1923-2005
Super symmetric field theories and integral modular functions.
with Stephan Stolz,
preprint 2007.
Topological 4-manifolds with geometrically 2-dimensional fundamental groups.
with Ian Hambleton and Matthias Kreck, preprint 2008.
Publications
New Constructions of Slice Links.
with Tim Cochran and Stefan Friedl, to appear in Commentarii Mathematici Helvetici 2008.
Positive topological field theories and manifolds of dimension > 4.
with Matthias Kreck, to appear in Journal of Topology, Volume 1, 2008.
Knot concordance and von Neumann rho-invariants.
with Tim Cochran, Duke Mathematical Journal, Volume 137, Number 2 (2007), 337--379.
Jacobi Identities in low-dimensional Topology.
with Jim Conant and Rob Schneiderman, Compositio Math. 143 (2007) 780-810.
Non-smoothable four-manifolds with infinite cyclic fundamental group.
with Stefan Friedl, Ian Hambleton and Paul Melvin, International Mathematics Research Notices, Vol. 2007, Article ID rnm031, 20 pages.
Geometric topology and connections with quantum field theory.
Abstracts from the workshop held June 12--18, 2005. Organized by Stephan Stolz and Peter Teichner. Oberwolfach Reports. Vol. 2, no. 2 (2005), 1505-1546.
What is an elliptic object?
with Stephan Stolz,
Topology, geometry and quantum field theory, London Math. Soc. LNS 308, Cambridge Univ. Press 2004, 247-343.
Generalized Cohomology and Supersymmetric Field Theories, Part 1, Peter Teichner
Generalized Cohomology and Supersymmetric Field Theories, Part 2, Stephan Stolz
Survey talks given at the Kavli Institute for Theoretical Physics Mathematical Structures in String Theory (Aug 1 - Dec 16, 2005)
New topologically slice knots.
with Stefan Friedl, Geometry and Topology, Vol.9 (2005), 2129-2158. - Correction to an example in the paper
On knots with trivial Alexander polynomial.
with Stavros Garoufalidis,
Journal of Differential Geometry 67 (2004), 763-789.
What is ... a grope?
Notices of the A.M.S. 51 (8) (2004), 892-893.
Whitney towers and the Kontsevich integral.
with Rob Schneiderman, Geometry and Topology Monogr. 7 (2004), 101-134.
3 Lectures on Whitney towers, Milnor invariants and concordance theory
21st Annual Workshop in Geometric Topology, Univ. of Wisconsin-Milwaukee, June 10-12, 2004.
Grope cobordism of classical knots.
with Jim Conant,
Topology, 43 (2004), 119-156.
Structure in the classical knot concordance group.
with Tim Cochran and Kent Orr,
Comment. Math. Helv. , 79 (2004), 105-123.
Grope cobordism and Feynman diagrams.
with Jim Conant,
Math. Annalen, 328 (2004), 135-171.
Knot concordance,
Whitney towers and von Neumann signatures.
with Tim Cochran and Kent Orr,
Annals of Math., 157 (2003), 433-519.
Flatness and the Ore condition for rings.
Proceedings of the AMS, 131 (2003), 1977-1980.
Knots, von Neumann Signatures, and Grope Cobordism.
Lecture given at the ICM 2002 in Beijing,
Proceedings of the International Congress of Math.,
Vol II: Invited Lectures, 437-446.
Higher order intersection numbers of 2-spheres in 4-manifolds.
with Rob Schneiderman, Algebraic & Geometric Topology, 1 (2000), 1-29.
All two dimensional links are null homotopic.
with Arthur Bartels, Geometry and Topology, 3 (1999), 235-252.
Symmetric surgery and boundary link maps.
Mathematische Annalen, 312 (1998), 717-735.
Maximal nilpotent quotients of 3-manifold groups.
Mathematical Research Letters 4 (1997), 283-293.
Betti number estimates for nilpotent groups.
with Michael Freedman and Richard Hain, Fields Medallists' Lectures, edited by M. Atiyah and D. Lagolnitzer,
World Sci. Ser. in 20th Century Math. 5 (1997), 413-434.
A non-extended hermitian form
over the group ring of the integers.
with Ian Hambleton, Manuscripta Mathematica 94 (1997), 435-442.
Alexander duality, gropes and
link homotopy.
with Slava Krushkal,Geometry and Topology, 1 (1997), 57-69.
4-Manifold Topology I.
with Michael Freedman,
Inventiones Mathematicae 122 (3) (1995), 509-529.
Appendix to 4-Manifold Topology I: Clarification of Linear Grope Height Raising.
with Michael Freedman,
Preprint 1995.
4-Manifold Topology II.
with Michael Freedman,
Inventiones Mathematicae 122 (3) (1995), 531-557.
Counterexamples to the Kneser conjecture in dimension four.
with Matthias Kreck and Wolfgang Lueck, Commentarii Mathematici Helvetici 70 (1995),
423-433.
Stable prime decompositions of four-manifolds.
with Matthias Kreck and Wolfgang Lueck, Commentarii Prospects in topology (Princeton, NJ, 1994), 251-269, Ann. of Math. Stud., 138, Princeton Univ. Press, Princeton, NJ, 1995.
Van Kampen's
embedding obstruction is incomplete for 2-complexes in 4-space.
with Slava Krushkal and Michael Freedman, Mathematical
Research Letters 1 (1994), 167-176.
6-Dimensional Manifolds without Totally Algebraic Homology.
Proceedings of the A.M.S. 123 (9) (1995), 2909-2914.
Nonorientable 4-manifolds with fundamental group of order 2.
with Ian Hambleton and Matthias Kreck, Transactions of the A.M.S. 344 (2) (1994), 649-665.
On the Star-Construction for Topological 4-Manifolds.
Proc. of the Georgia International Topology
Conference 1993. Geom. top. AMS/IP Stud. Adv. Math. 2 300-312 A.M.S. (1997)
On the signature of four-manifolds with universal covering spin.
Mathematische Annalen 295 (1993), no. 4, 745-759.
Topological 4-manifolds with finite fundamental group.
PhD Thesis, University of Mainz, Germany, Shaker Verlag 1992, ISBN 3-86111-182-9.
Unpublished papers
Classification of closed topological 4-manifolds.
A short and incomplete survey from 1992.
All oriented 4-manifolds have spin-c structures.
with Elmar Vogt,
Preprint 1994.