Teaching Research Papers Links
Teaching (Spring 11)
I am currently teaching Level 4 Algebraic Topology and E2N (numerical methods in engineering). I am also coordinating Level 3 Writing and Presenting Mathematics.
Research
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.
I am currently teaching Level 4 Algebraic Topology and E2N (numerical methods in engineering). I am also coordinating Level 3 Writing and Presenting Mathematics.
Research
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.
Papers
- (with
S.
Strle) Dehn surgeries and negative-definite four-manifolds (in
preparation).
On
slicing
numbers
of
knots,
Transactions
of
the
American
Mathematical Society, Vol. 362 (2010), pages 3095--3106.- (with
S.
Strle)
A
characterisation
of the Z^n + Z(\delta) lattice and
definite nonunimodular intersection forms, arXiv:0802.1495.
(Submitted for publication.)
- (with
C. Manolescu) A concordance invariant from the Floer homology of double
branched covers, International
Mathematics
Research
Notices
2007
2007: rnm077-21.
- Unknotting
information
from
Heegaard
Floer
homology, Advances
in
Mathematics,
Vol.
217
(2008),
pages
2353 -- 2376.
- (with
S. Strle) Definite manifolds bounded by rational homology three
spheres, ``Geometry
and
Topology
of
Manifolds'',
Fields Institute Communications, Vol. 47,
AMS (2005), pages 243 -- 252.
- (with
S. Strle) A characterisation of the n<1>+<3>
form
and applications to rational homology spheres, Mathematical
Research
Letters,
Vol.
13
(2006), pages 259 -- 271.
- (with
S. Strle) Rational homology spheres and the four-ball genus of knots, Advances
in
Mathematics,
Vol.
200
(2006), pages 196 -- 216.
- Instantons
on
cylindrical
manifolds
and
stable
bundles,
Geometry and Topology, Vol. 5 (2001) Paper no. 24, pages 761--797.