Bredon cohomology methods in mass partition problems on spheres
Abstract
We apply $\mathrm{RO}(G)$-graded Bredon cohomology to mass assignment problems, extending classical mass partition methods. Within this framework, we reprove a recent result of Lessure and Soberón: for $n+1$ mass assignments on $k$-dimensional affine subspaces of $\mathbb{R}^n$, there exists a $k$-subspace containing a sphere that simultaneously bisects all measures. This approach highlights a flexible topological framework with potential for broader applications.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Point processes and geometric inequalities
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 February 2026
- Language
- EN
- Document type
- Preprint