Bredon cohomology methods in mass partition problems on spheres

Surojit Ghosh

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arXiv · 2602.21842

Bredon cohomology methods in mass partition problems on spheres

Surojit Ghosh

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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 Sober\'on: 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.

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Surojit Ghosh. 2026-02-25. Bredon cohomology methods in mass partition problems on spheres. https://arxiv.org/abs/2602.21842

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