Preprints
Immersions of punctured 4-manifolds
with Michael Freedman, Daniel Kasprowski and Matthias Kreck, arXiv:2208.03064
The Kervaire-Milnor invariant in the stable classification of spin 4-manifolds
with Daniel Kasprowski and Mark Powell, arXiv:2105.12153
The 4-dimensional disk embedding theorem and dual spheres
with Mark Powell and Arunima Ray, arXiv:2006.05209
Clasper concordance, Whitney towers and repeating Milnor invariants
with Jim Conant and Rob Schneiderman, arXiv:2005.05381
Non-local spin field theories in dimension three
with Matthias Kreck and Stephan Stolz, Preprint 2014
Selected Publications
A new approach to light bulb tricks: Disks in 4-manifolds
with Danica Kosanovic, to appear in Duke Math. Journal.
A space level light bulb theorem in all dimensions
with Danica Kosanovic, to appear in Commentarii Math. Helv.
Embedding surfaces in 4-manifolds
with Daniel Kasprowski, Mark Powell and Arunima Ray, to appear in Geometry & Topology.
Algebraic criteria for stable diffeomorphism of spin 4-manifolds
with Daniel Kasprowski and Mark Powell, to appear in Memoirs of the AMS.
Homotopy versus Isotopy: Spheres with duals in 4-manifolds
with Rob Schneiderman, Duke Math. Journal 171, No. 2, 2022, 273-325.
The group of disjoint 2-spheres in 4-space
with Rob Schneiderman, Annals of Mathematics, Vol. 190, 2019, 669-750.
Milnor invariants and twisted Whitney towers
with Jim Conant and Rob Schneiderman, Journal of Topology 7, 2014, 187-224.
Whitney tower concordance of classical links
with Jim Conant and Rob Schneiderman, Geometry & Topology, 16, 2012, 1419-1479.
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. 2011, 279-340.
From minimal geodesics to super symmetric field theories
In memory of Raoul Bott, with Henning Hohnhold and Stephan Stolz
CRM Proceedings and Lecture Notes 50, 2010, 207-273.
with Stephan Stolz, Topology, geometry and quantum field theory,
London Math. Soc. LNS 308, Cambridge Univ. Press 2004, 247-343.
Grope cobordism and Feynman diagrams
with Jim Conant, Math. Annalen 328, 2004, 135-171.
Knot concordance and von Neumann rho-invariants
with Tim Cochran, Duke Math. Journal 137, 2007, 337-379.
Knot concordance, Whitney towers and signatures
with Tim Cochran and Kent Orr, Annals of Mathematics, 157, 2003, 433-519.
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.
with Michael Freedman, Inventiones Math. 122, 1995, 509-529.
Appendix: Clarification of linear grope height raising.
with Michael Freedman, Inventiones Math. 122, 1995, 531-557.
Published Papers
Homotopy versus isotopy: 2-spheres in 5-manifolds
with Danica Kosanovic and Rob Schneiderman, to appear in Pacific Math. Journal.
A new approach to light bulb tricks: Disks in 4-manifolds
with Danica Kosanovic, to appear in Duke Math. Journal 2024.
A space level light bulb theorem in all dimensions
with Danica Kosanovic, to appear in Commentarii Math. Helv., 2024.
The 4-dimensional surface embedding theorem
with Daniel Kasprowski, Mark Powell and Arunima Ray, to appear in Geometry & Topology, 2023.
Algebraic criteria for stable diffeomorphism of spin 4-manifolds
with Daniel Kasprowski and Mark Powell, to appear in Memoirs of the AMS 2023.
4-manifolds up to connected sums with complex projective planes
with Daniel Kasprowski and Mark Powell, American Journal of Math. 144, No.1, 2022, 75-118.
Homotopy versus Isotopy: Spheres with duals in 4-manifolds
with Rob Schneiderman, Duke Math. Journal 171, No. 2, 2022, 273-325.
with Min Hoon Kim and Mark Powell, Pure and Applied Math. Quarterly, Volume 17, No. 1, 2021, 237-247.
CP^2-stable classification of 4-manifolds with finite fundamental group
with Daniel Kasprowski, Pacific Journal of Math. Vol. 310, No. 2, 2021, 355-373.
The group of disjoint 2-spheres in 4-space
with Rob Schneiderman, Annals of Mathematics, Vol. 190, No. 3, 2019, 669-750.
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 7, 2014, 187-224.
with Rob Kirby and Paul Melvin,
Proceedings of the Freedman Fest, Geometry & Topology Monographs 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 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. 2011, 279-340.
Differential forms and 0-dimensional super symmetric field theories
with Henning Hohnhold, Matthias Kreck and Stephan Stolz, Quantum Topology 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 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 Math. Helvetici, vol. 84 (3) 2009, 617-638
Positive topological field theories and manifolds of dimension > 4.
with Matthias Kreck, Journal of Topology 1 (2008), 663-670.
Knot concordance and von Neumann rho-invariants
with Tim Cochran, Duke Math. Journal 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 Math. 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.
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 Monograph 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 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