Concordance and isotopy invariants of surfaces. Notes on selected invariants of surfaces in 4-manifolds, prepared for a mini-course at the Banff conference Topology in dimension 4.5.
Spanning 3-discs in the 4-sphere pushed into the 5-disc. A note outlining a proof via surgery theory that any two spanning 3-discs for the trivial 2-knot in the 4-sphere become smoothly isotopic rel. boundary after pushing their interiors into the 5-disc.
Classification of closed, oriented, topological 4-manifolds with infinite cyclic fundamental group. Notes from an expository talk at MPIM, which explain the classification using the surgery exact sequence.
Linking forms of amphichiral knots, with Stefan Friedl and Allison N. Miller. A preprint that we wrote before discovering that the main corollary had been proven by Goeritz in 1933. It is somewhat surprising that this method of detecting chirality does not appear in modern knot theory textbooks.
A survey of the work of Cochran-Orr-Teichner on knot concordance, which was chapter 7 of my thesis.
Lecture notes on Slice Knots based on a course given by Peter Teichner in 2001 which Julia Collins and I typed up at the beginning of our PhD studies.
Some notes on constructing duality chain equivalences for some simple manifolds, in the sense that the word problem is easy for their fundamental groups.
An expository note on the basic operation which removes intersections of immersed surfaces in 4-manifolds.
The Manifold Atlas page on the Blanchfield form.
Notes on the Borsuk-Ulam Theorem which give a proof using chain complexes, and on which I based a Geometry Club talk at Edinburgh.