My research is in low-dimensional topology. I am interested in smooth 3-manifolds, 4-manifolds and knots, and in the use
of gauge-theoretic invariants of manifolds, especially Floer homology groups.
Mathematical genealogy. Papers
You can also find my papers on the
and on zbMATH.
Immersed disks, slicing numbers and concordance unknotting numbers,
Comm. Anal. Geom. 24 (2016), no. 5, 1107--1138. (with
Unlinking information from 4-manifolds,
Bull. London Math. Soc. 47 (2015), no. 6, 964--979. (with
Signatures, Heegaard Floer correction terms and quasi-alternating links,
Proc. Amer. Math. Soc. 143 (2015), no. 2, 907--914. (with
R. Bieri and
On subsets of S,
n whose (n+1)-point subsets are contained in open hemispheres New York J. Math. 20 (2014), 1021--1041. (with
Concordance groups of links,
Algebr. Geom. Topol. 12 (2012), no. 4, 2069--2093. (with
Dehn surgeries and negative-definite four-manifolds,
Selecta Math. (N.S.) 18 (2012), no. 4, 839--854. (with
A characterisation of the Z,
n⊕ Z(δ) lattice and definite nonunimodular intersection forms
Amer. J. Math. 134 (2012), no. 4, 891--913.
On slicing invariants of knots,
Trans. Amer. Math. Soc. 362 (2010), no. 6, 3095--3106.
Unknotting information from
Heegaard Floer homology,
Adv. Math. 217 (2008), no. 5, 2353--2376. (with
A concordance invariant from the Floer homology of double branched covers,
Int. Math. Res. Not. IMRN 2007, no. 20, Art. ID rnm077, 21 pp. (with
A characterisation of the n〈1〉⊕〈3〉 form and
applications to rational homology spheres,
Math. Res. Lett. 13 (2006), no. 2, 259--271. (with
Rational homology spheres and the four-ball genus of knots,
Adv. Math. 200 (2006), no. 1, 196--216. (with
Definite manifolds bounded by rational homology three spheres,
``Geometry and Topology of Manifolds'', Fields Institute
Communications, Vol. 47, AMS (2005), pages 243--252.
Instantons on cylindrical manifolds and stable bundles,
Geometry and Topology, Vol. 5 (2001) Paper no. 24, pages 761--797.
2015-16 Semester 2
A maple program for computing the d-invariants of a positive semi-definite symmetric matrix.
You may need to remove the .xml extension from the downloaded file before use. (Written jointly with S. Strle.)
Mathematica programs to compute the Goeritz matrices of a link, and also to compute signature and nullity of a symmetric matrix, or of a link.
A maple program for computing the Levine-Tristram signature function of a torus knot (based on Litherland's paper).
You may need to remove the .xml extension from the downloaded file before use.