3 papers
math.GT2026
A counterexample to a conjecture of Plotnick on knot exteriors
Tommy Hofmann, John Nicholson
We resolve a conjecture of S. Plotnick from 1983 concerning the homotopy type of four-dimensional knot complements. We show that the exteriors of two branched twist spins of the tr…
math.GR2025
Exotic presentations of quaternion groups and Wall's D2 problem
Tommy Hofmann, John Nicholson
The D2 problem of C. T. C. Wall asks whether every finite cohomologically 2-dimensional CW-complex is homotopy equivalent to a finite 2-complex. Several potential counterexamples h…
math.AT2025
Swan modules and homotopy types after a single stabilisation
Tommy Hofmann, John Nicholson
We study Swan modules, which are a special class of projective modules over integral group rings, and their consequences for the homotopy classification of CW-complexes. We show th…