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




Selected Publications


Homotopy versus Isotopy: Spheres with duals in 4-manifolds

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


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.


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.


Grope cobordism and Feynman diagrams

with Jim Conant, Mathematische Annalen 328, 2004, 135-171.


Knot concordance and von Neumann rho-invariants

with Tim Cochran, Duke Mathematical 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 Int. Congress of Math.,Vol II: Invited Lectures, 437-446.


4-manifold topology I

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

Appendix: Clarification of linear grope height raising.


4-manifold topology II

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



Published Papers



Homotopy versus Isotopy: Spheres with duals in 4-manifolds

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


The group of disjoint 2-spheres in 4-space

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


The round handle problem

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, Pacific Journal of Math. Vol. 310, No. 2 (2021), 355-373.


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.


Cohomotoy sets of 4-manifolds

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.


Traces in monoidal categories

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 Mathematici 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 Mathematical 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 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.


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.


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, Mathematische 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)


4-manifold topology I

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

Appendix: Clarification of linear grope height raising.


4-manifold topology II

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