Preprints

Algebraic criteria for stable diffeomorphism of spin 4-manifolds

with Daniel Kasprowski and Mark Powell, 76 pages, Preprint 2020.

The 4-dimensional disk embedding theorem and dual spheres

with Mark Powell and Arunima Ray, 36 pages, Preprint 2020.

Clasper concordance, Whitney towers and repeating Milnor invariants

with Jim Conant and Rob Schneiderman, 30 pages, Preprint 2020.

4-manifolds up to connected sums with complex projective planes

with Daniel Kasprowski and Mark Powell, 36 pages, Preprint 2018.

Non-local spin field theories in dimension three

with Matthias Kreck and Stephan Stolz, Preprint 2014

Published Papers

The group of disjoint 2-spheres in 4-space

with Rob Schneiderman, Annals of Mathematics, Vol. 190, No. 3 (2019), 669-750.

Homotopy versus Isotopy: Spheres with duals in 4-manifolds

with Rob Schneiderman, to appear in Duke Math. Journal 2021.

with Min Hoon Kim and Mark Powell, to appear in Pure and Applied Mathematics Quarterly 2021.

CP^2-stable classification of 4-manifolds with finite fundamental group

with Daniel Kasprowski, to appear in Pacific Journal of Math. 2021.

Stable classification of 4-manifolds with 3-manifold fundamental groups

with Daniel Kasprowski, Markus Land and Mark Powell, Journal of Topology 10 (2017), 827-881.

Cochran invariants via twisted Whitney towers

with Jim Conant and Rob Schneiderman, Journal of Knot Theory and Its Ramifications Vol. 26 (2017) 28 pages, commemorative issue to honor Tim Cochran.

Geometric filtrations of String Links and Homology Cylinders

with Jim Conant and Rob Schneiderman, Quantum Topology, Volume 7 (2016), 281-328.

Pulling apart 2-spheres in 4-manifolds

with Rob Schneiderman, Documenta Math. 19 (2014) 941-992.

Milnor invariants and twisted Whitney towers

with Jim Conant and Rob Schneiderman, Journal of Topology (2014) 7 (1): 187-224.

with Rob Kirby and Paul Melvin,

Proceedings of the Freedman Fest, Geometry & Topology Monographs, Volume 18 (2012), 161-190.

Universal quadratic forms and Whitney tower intersection invariants

with Jim Conant and Rob Schneiderman,

Proceedings of the Freedman Fest, Geometry & Topology Monographs, Volume 18 (2012), 35-60.

Whitney tower concordance of classical links

with Jim Conant and Rob Schneiderman, Geometry & Topology, 16, 2012, 1419-1479.

Tree homology and a conjecture of Levine

with Jim Conant and Rob Schneiderman, Geometry & Topology, 16, 2012, 555-600.

with Stephan Stolz, Transactions of the A.M.S. 364, 2012, 4425-4464.

Higher order intersections in low-dimensional topology

with Jim Conant and Rob Schneiderman, Proc. of the National Academy 2011, 108 (20) 8131-8138.

Supersymmetric field theories and generalized cohomology.

with Stephan Stolz, Mathematical Foundations of Quantum Field Theory and Perturbative String Theory, Proceedings of Symposia in Pure Mathematics,Vl.83, AM.S. 201, 29-340.

Differential forms and 0-dimensional super symmetric field theories

with Henning Hohnhold, Matthias Kreck and Stephan Stolz, Quantum Topol. 2 (2011), 1-41.

Super manifolds - a short and incomplete survey.

with Henning Hohnhold and Stephan Stolz,Bulletin of the Manifold Atlas 2011, 1-6.

From minimal geodesics to super symmetric field theories.

In memory of Raoul Bott, with Henning Hohnhold and Stephan Stolz

CRM Proceedings and Lecture Notes, Volume 50, 2010, 207-273.

Topological 4-manifolds with geometrically 2-dim. fundamental groups.

with Ian Hambleton and Matthias Kreck, Journal of Topology and Analysis, vol. 1 (2) 2009, 123-151

New constructions of slice links.

with Tim Cochran and Stefan Friedl, Commentarii Mathematici Helvetici, vol. 84 (3) 2009, 617-638

Positive topological field theories and manifolds of dimension > 4.

with Matthias Kreck, Journal of Topology, Volume 1 (2008), 663-670.

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.

with Stephan Stolz, Topology, geometry and quantum field theory,

London Math. Soc. LNS 308, Cambridge Univ. Press 2004, 247-343.

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.

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.

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 signatures.

with Tim Cochran and Kent Orr, Annals of Mathematics, Volume 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 2-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 93 (1997), 435-442.

Alexander duality, gropes and link homotopy.

with Slava Krushkal,Geometry and Topology, 1 (1997), 57-69.

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)

with Michael Freedman, Inventiones Mathematicae 122 (3) (1995), 509-529.

Appendix: Clarification of linear grope height raising.

with Michael Freedman, Inventiones Mathematicae 122 (3) (1995), 531-557.

Counter examples to the Kneser conjecture in dimension four.

with Matthias Kreck and Wolfgang Lueck,

Commentarii Mathematici Helvetici 70 (1995), 423-433.

Stable prime decompositions of 4-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.

6-Dimensional manifolds without totally algebraic homology.

Proceedings of the A.M.S. 123 (9) (1995), 2909-2914.

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.

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 signature of 4-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

All oriented 4-manifolds have spin-c structures.

with Elmar Vogt, Preprint 1994