Preprints:
Papers accepted for publication:
- Minimal Genus in 4-manifolds with a Free Circle Action
(with Stefano Vidussi)
to be published by Advances in Mathematics,
20 pages. Version 08/12
- Rank gradients of infinite cyclic covers of 3-manifolds
(with Jason Deblois and Stefano Vidussi)
to be published by the Michigan Journal of Mathematics,
15 pages. Version 12/12
- The virtual fibering theorem for 3-manifolds (with Takahiro Kitayama)
to be published by L'enseignement mathematicque, 23 pages. Version 10/12
- A note on the growth of Betti numbers and ranks of 3-manifold groups
to be published by the Bulletin des Sciences Mathematiques, 9 pages. Version 8/12
- The unknotting number and classical invariants II
(with Maciej Borodzik)
to be published by the Glasgow Journal of Mathematics,
26 pages. Version 8/13
- Metabelian SL(n,C) representations of knot groups, III: deformations,
(with Hans Boden)
to be published by the Quarterly Journal of Mathematics., 22 pages. Version 08/12
- Twisted Reidemeister torsion, the Thurston norm and fibered manifolds
to be published by Geometriae Dedicata,
10 pages. Version 12/12
- The Thurston norm and twisted Alexander polynomials (with Stefano Vidussi)
to be published by the Journal fur Reine und Angewandte Mathematik, 17 pages. Version 06/12.
- Kaehler groups, quasi-projective groups, and 3-manifold groups
(with Alexander Suciu)
to be published by the Journal of the London Mathematical Sociecty,
18 pages. Version 12/12
- Metabelian SL(n,C) representations of knot groups IV: Twisted Alexander polynomials
(with Hans Boden)
to be published by the Mathematical Proceedings of the Cambridge Philosophical Society, 21 pages. Version 9/12
- A note on a topological approach to the mu-constant problem in dimension 2 (with Maciej Borodzik)
to be published by Revista Matematica Complutense, 6 pages. Version 3/12
- On the topology of Symplectic Calabi-Yau 4-manifolds (with Stefano Vidussi)
to be published by the Journal of Topology, 12 pages. Version 3/13.
- Links Not Concordant to the Hopf Link (with Mark Powell)
to be published by the Math. Proc. Camb. Phil. Soc., 40 pages. Version 05/11
- A Vanishing Theorem for Twisted Alexander Polynomials with Applications to Symplectic 4-manifolds
(with Stefano Vidussi)
to be published by the Journal of the European Mathematical Society, 15 pages. Version 08/12
- Cobordisms to weakly splittable links
(with Mark Powell)
to be published by Proc. Amer. Math. Soc.
11 pages. Version 12/11
Publications:
- Taut sutured manifolds and twisted homology (with Taehee Kim)
Mathematical Research Letter 20 (2013), no. 02, 1-15.
- Commensurability of knots and L^2 invariants
to be published by the Proceedings of Geometry and Topology Down Under: The Rubinstein birthday conference.
Contemporary Mathematics 597 (2013), 263-279.
- 3-manifold groups are virtually residually p (with Matthias Aschenbrenner)
Memoirs Amer. Math. Soc. Vol 225 (2013), 106 pages.
- Twisted torsion invariants and link concordance
(with Jae Choon Cha)
Forum Mathematicum 25 (2013), 471-504.
- Poincare duality and degrees of twisted Alexander polynomials (with Taehee Kim and Takahiro Kitayama)
Indiana University Mathematics Journal 61 (2012), 147-192.
- Twisted Alexander polynomials of hyperbolic knots
(with Nathan Dunfield and Nicholas Jackson)
Experimental Mathematics 21 (2012), 329-352.
the program written by Nathan Dunfield and the full data can be found on Nathan's webpage
- Cosmetic crossings and Seifert matrices
(with Cheryl Balm, Efstratia Kalfagianni and Mark Powell)
Communications in Analysis and Geometry 20 (2012), 235–253.
- Construction of symplectic structures on 4-manifolds with a free circle action (with Stefano Vidussi)
Proc. Royal Soc. Edinburgh: Section A 142 (2012), pp 359 - 370.
-
An Injectivity Theorem for Casson-Gordon Type Representations relating to the Concordance of Knots and Links
(with Mark Powell)
Bull. Korean Math. Soc. 49 (2012), No. 2, pp. 395-409
- Twisted Alexander polynomials and fibered 3-manifolds
(with Stefano Vidussi)
Low-Dimensional and Symplectic Topology, Proceedings of Symposia in Pure Mathematics
Volume 82 (2011), 111-130.
- The decategorification of sutured Floer homology
(with Andras Juhasz and Jacob Rasmussen)
Journal of Topology (2011) 4(2): 431-478
-
The cobordism group of homology cylinders (with Jae Choon Cha and Taehee Kim)
Compositio Mathematica 147 (2011), 914-942
- Symplectic 4-manifolds with K=0 and the Lubotzky alternative (with Stefano Vidussi)
Mathematics Research Letters 18 (2011) 513-519
- Residual properties of graph manifold groups (with Matthias Aschenbrenner)
Topology and its Applications 158 (2011) 1179-1191
-
Twisted Alexander polynomials detect fibered 3-manifolds (with Stefano Vidussi)
Annals of Mathematics, Volume 173 (2011), 1587-1643
- A criterion for HNN extensions of finite p-groups to be residually p (with Matthias Aschenbrenner)
Journal of Pure and Applied Algebra 215 (2011) 2280–2289
-
Metabelian SL(n,C) representations of knot groups II: fixed points (with Hans Boden)
Pacific Journal of Mathematics, 249 (2011), 1-10
- A survey of twisted Alexander polynomials
(with Stefano Vidussi)
The Mathematics of Knots: Theory and Application (Contributions in Mathematical and Computational Sciences), editors:
Markus Banagl and Denis Vogel (2010), p. 45-94.
-
Realizations of Seifert matrices by hyperbolic knots
J. Knot Theory and its Ramifications Volume 18 (2009), 1471-1474
-
L^2-Betti numbers of plane algebraic curves (with Constance Leidy and Laurentiu Maxim)
Michigan Math. Journal, 58 (2009), no. 2, 291-301
-
New constructions of slice links (with Tim Cochran and Peter Teichner)
Comment. Math. Helv. Volume 84, Issue 3 (2009), 617-638
-
Twisted Alexander polynomials, symplectic 4-manifolds and surfaces of minimal complexity (with Stefano Vidussi)
Banach Center Publ. 85 (2009), 43-57
-
Metabelian SL(n,C) representations of knot groups (with Hans Boden)
Pac. J. Math, Vol. 238, 7-25 (2008)
- Twisted Alexander norms give lower
bounds on the Thurston norm (with Taehee Kim)
Trans. Amer. Math. Soc. 360 (2008), 4597-4618
-
Twisted Alexander polynomials and symplectic structures (with Stefano Vidussi)
Amer. J. Math. 130, 455-484 (2008)
-
The parity of the Cochran-Harvey invariants of 3-manifolds (with Taehee Kim)
Trans. Amer. Math. Soc. 360 (2008), 2909-2922.
-
Symplectic S^1 x N^3, surface subgroup separability, and totally degenerate Thurston norm (with Stefano Vidussi)
Journal Amer. Math. Soc. 21 (2008), 597-610.
-
Nontrivial Alexander polynomials of knots and links (with Stefano Vidussi)
Bull. London Math. Soc., Vol. 39: 614-622 (2007)
-
Non-smoothable four-manifolds with cyclic fundamental group (with Ian Hambleton, Paul Melvin, Peter Teichner)
Inter. Math. Res. Not., Vol. 2007, Article ID rnm031, 20 pages
- Reidemeister torsion, the Thurston norm and Harvey's invariants
Pacific Journal
of Mathematics, Vol. 230: 271-296 (2007)
-
Non-commutative Multivariable Reidemeister Torsion and the Thurston Norm (with Shelly Harvey)
Alg. Geom. Top., Vol. 7: 755-777 (2007)
- Algorithm for finding boundary link Seifert matrices
Journal of Knot Theory and its Ramifications, Vol 15, No. 5: 601-612 (2006)
-
The Thurston norm, fibered manifolds and
twisted Alexander polynomials (with Taehee Kim)
Topology 45: 929-953 (2006)
- New topologically slice knots (with Peter Teichner)
Geometry and Topology, Volume 9 (2005) Paper no. 48, pages 2129-2158
and the correction to an example
Correction to ‘New topologically slice knots’
Geometry and Topology, Volume 10 (2006) 3001–3004
and another
erratum
- Full signature invariants for L_0(F(t))
Proc. Amer. Math. Soc. 133: 647-653 (2005)
-
L^2-eta-invariants and their approximation by unitary eta-invariants
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 138: 327-338 (2005)
-
Link concordance, boundary link concordance and eta-invariants
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 138: 437-460 (2005)
-
Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants
Algebraic and Geometric Topology, Vol. 4: 893-934 (2004)
Note that the versions which appear in the journals are considered the final versions. The above versions are the
preprint versions.
Papers in non-refereed publications:
-
Symplectic S^1 x N^3 and subgroup separability (with Stefano Vidussi)
Oberwolfach Reports,
Volume 3, Issue 3 (2006), 2166 - 2168
-
Fundamental groups of 3-manifolds (on joint work with Matthias Aschenbrenner)
Oberwolfach Reports, Volume 7, Issue 3 (2010), 2479-2482
- Centralizers in 3-manifold groups
RIMS Kokyuroku 1747 (2011), 23-34
- Approximations to the hyperbolic volume of knots (with Nicholas Jackson)
13 pages, RIMS Kokyuroku 1747 (2011), 35-46
- Cobordism on homology cylinders and combinatorial torsions
(with Jae Choon Cha and Taehee Kim)
RIMS Kokyuroku 1747 (2011), 17-22
Lecture notes:
Videos from talks
- Symplectic 4-manifolds of the form S^1xN, Chern Centennial Conference, November 2011, MSRi
- The algebraic unknotting number, University of Edinburgh, February 2012.
- Minimal genus surfaces in 4-manifolds with a free S^1-action, KAIST, August 2012.
- Topologically slice knots, University of Edinburgh, July 2013.
- Splittings of knot groups, Geometric Topology in New York, August 2013.
Slides and talks:
- Complexity of surfaces in 4-manifolds with a free circle action, University of Akron, October 2012
- The algebraic unknotting number, University of Edinburgh, February 2012
et aussi le nombre de denouage algebrique a Paris VII Mars 2012
- Minimal genus Seifert surfaces are robust, University of Warwick, February 2012.
-
A survey of twisted Alexander polynomials, Akita, September 2010.
-
Twisted Alexander, fibered 3-manifolds and the Thurston norm, Akita, September 2010.
-
Twisted Alexander polynomials of hyperbolic knots, AMS-KMS joint conference, Seoul, December 2009.
-
Les varietes fibrees de dimension trois et les varietes symplectiques de dimension quatre, Conference a Paris VII, Mai 2009.
-
Symplectic 4-manifolds and fibered 3-manifolds,
talk at the 5th East Asian conference on knots, January 2009.
-
Symplectic 4-manifolds and fibered 3-manifolds,
talk at Brandeis University, June 2008
-
New examples of topologically slice knots and links,
talk at the University of Waterloo, November 2007
-
Symplectic 4-manifolds and fibered 3-manifolds,
talk at the Low Dimensional Geometry and Topology Symposium at Warwick 2007
-
4-manifolds and their (equivariant) intersection forms,
talk at University of California at Riverside 2007
-
Commensurabiliy and L^2-invariants,
talk at Columbia University 2007
- Twisted Alexander polynomials and Symplectic Structures,
talk in Baton Rouge 2006 on joint work with Stefano Vidussi
- Twisted Alexander polynomials, the Thurston norm and symplectic manifolds,
talk at UC-Berkeley 2005 on joint work with Taehee Kim and Stefano Vidussi
- Examples of topologically slice knots,
talk in Edinburgh 2005 on joint work with Peter Teichner
Miscellaneous notes:
- Primzahltests und Faktorisierungsmethoden,
Zulassungsarbeit fuer das Staatsexamen fuer Lehramt Gymnasium, Regensburg (1997)
- The group law on elliptic curves, part of my undergraduate
thesis,
Regensburg (1998)
-
Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants , PhD thesis, Brandeis
University (2003)
-
Symplectic 4-manifolds with a free circle action (with Stefano Vidussi)
this paper was split into several papers, parts of it appear in
'Construction of symplectic structures on 4-manifolds with a free circle action' and in
`Symplectic 4-manifolds with K=0 and the Lubotzky alternative'
- The Thurston norm, fibered manifolds and
twisted Alexander polynomials (more detailed version of the above paper with 51 pages)
- Alexander polynomials of plane algebraic curves, 21 pages.
A note slightly generalizing results of Cogolludo-Florens and Leidy-Maxim (2005)
- Hyperbolic examples of topologically slice knots, 5 pages (2007)
- Notes taken at a talk by Dani Wise on
`The structure of groups with a quasi-convex hierarchy' in Montreal, 21 pages (April 2010)
- Concordance of links and their components, 2 pages (April 2011)
- 3-manifolds after Perelman, 12 pages, extended version
of a talk given at the Max-Planck institute in Bonn (October 2011)