92 citations · 147 across the 10 of their papers we have counts for
11 papers
On the intersection ring of graph manifolds
Margaret I. Doig, Peter D. Horn
We calculate the intersection ring of three-dimensional graph manifolds with rational coefficients and give an algebraic characterization of these rings when the manifold's underly…
On computing higher-order Alexander modules of knots
Peter D. Horn
Cochran defined the nth-order integral Alexander module of a knot in the three sphere as the first homology group of the knot's (n+1)th-iterated abelian cover. The case n=0 gives t…
Structure in the bipolar filtration of topologically slice knots
Tim D. Cochran, Peter D. Horn
Let T denote the group of smooth concordance classes of topologically sice knots. We show that the first quotient in the bipolar filtration of T (i.e. 0-bipolar knots modulo 1-bipo…
Filtering smooth concordance classes of topologically slice knots
Tim D. Cochran, Shelly Harvey, Peter Horn
We propose and analyze a structure with which to organize the difference between a knot in the 3-sphere bounding a topologically embedded 2-disk in the 4-ball and it bounding a smo…
Knot concordance and homology cobordism
Tim D. Cochran, Bridget D. Franklin, Matthew Hedden +1
We consider the question: "If the zero-framed surgeries on two oriented knots in the 3-sphere are integral homology cobordant, preserving the homology class of the positive meridia…
Rational knot concordance and homology cobordism
Tim D. Cochran, Bridget D. Franklin, Peter D. Horn
The following is a long-standing open question: "If the zero-framed surgeries on two knots in the 3-sphere are integral homology cobordant, are the knots themselves concordant?" We…