1 citations · 1 across the 4 of their papers we have counts for
9 papers
The Hausmann-Weinberger 4-manifold invariant of abelian groups
Paul Kirk, Charles Livingston
The Hausmann-Weinberger invariant of a group G is the minimal Euler characteristic of a closed orientable 4-manifold M with fundamental group G. We compute this invariant for finit…
A survey of classical knot concordance
Charles Livingston
This is survey about the classical knot concordance group, prepared for an upcoming handbook of knot theory. Topics include: the basic definitions of concordance; the theory of alg…
Four-manifolds of large negative deficiency
Charles Livingston
For every N > 0 there exists a group of deficiency less than -N that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the compleme…
Knot signature functions are independent
Jae Choon Cha, Charles Livingston
To each unit complex number with positive imaginary part there is defined a Tristram-Levine knot signature function. The set of all such signature functions is linearly independent…
Observations on Lickorish knotting of contractible 4-manifolds
Charles Livingston
Lickorish has constructed large families of contractible 4--manifolds that have knotted embeddings in the 4--sphere and has also shown that every finitely presented perfect group w…
Pseudo-slice knots
Charles Livingston
For n >1, if the Seifert form of a knotted 2n-1 sphere K in S^{2n+1} has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three (n =…