We give a short introduction to the theory of twisted Alexander polynomials of a 3-manifold
associated to a representation of its fundamental group. We summarize their formal …

Based on Fields medal winning work of Michael Freedman, this book explores the disc
embedding theorem for 4-dimensional manifolds. This theorem underpins virtually all our …

Knot concordance and higher-order Blanchfield duality Page 1 Geometry & Topology 13 (2009)
1419–1482 1419 Knot concordance and higher-order Blanchfield duality TIM DCochran …

Let CT be the subgroup of the smooth knot concordance group generated by topologically
slice knots and let CΔ be the subgroup generated by knots with trivial Alexander polynomial …

For each sequence P=(p_1 (t), p_2 (t),\dots) of polynomials we define a characteristic series
of groups, called the derived series localized at P. These group series yield filtrations of the …

We give a new proof that the Levine–Tristram signatures of a link give lower bounds for the
minimal sum of the genera of a collection of oriented, locally flat, disjointly embedded …

We make use of the action of $ H_1 (Y) $ in Heegaard Floer homology to generalize the
Ozsv\'ath-Szab\'o correction terms for $3 $-manifolds with standard $\operatorname …

We define a set of “second-order” L (2)–signature invariants for any algebraically slice knot.
These obstruct a knot's being a slice knot and generalize Casson–Gordon invariants, which …

We give a formula for the duality structure of the 3–manifold obtained by doing zero-framed
surgery along a knot in the 3–sphere, starting from a diagram of the knot. We then use this to …

We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the
attaching circle, and we prove disc embedding results for height 2 and 3 Casson towers …