Positive curvature, torus symmetry, and matroids

Kennard, Lee; Wiemeler, Michael; Wilking, Burkhard

Research article (journal) | Peer reviewed

Abstract

We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour’s 1980 classification of the former objects, we obtain a classification of the latter. In addition, we prove optimal upper bounds for the cogirth of regular matroids up to rank 9, and we apply this to prove the existence of fixed-point sets of circles with large dimension in a torus representation with this property up to rank 9. Finally, we apply these results to prove new obstructions to the existence of Riemannian metrics with positive sectional curvature and torus symmetry.

Details about the publication

JournalJournal of the European Mathematical Society (JEMS)
StatusPublished
Release year2025
DOI10.4171/JEMS/1656
Keywords positive sectional curvature; torus action; matroid; cogirth; graph systole

Authors from the University of Münster

Wiemeler, Michael
Professur für Differentialgeometrie (Prof. Wilking)
Wilking, Burkhard
Professur für Differentialgeometrie (Prof. Wilking)