# Geometric coincidence results from multiplicity of continuous maps

@article{Karasev2011GeometricCR, title={Geometric coincidence results from multiplicity of continuous maps}, author={Roman N. Karasev}, journal={arXiv: Geometric Topology}, year={2011} }

In this paper we study geometric coincidence problems in the spirit of the following problems by B. Gr\"unbaum: How many affine diameters of a convex body in $\mathbb R^n$ must have a common point? How many centers (in some sense) of hyperplane sections of a convex body in $\mathbb R^n$ must coincide?
One possible approach to such problems is to find topological reasons for multiple coincidences for a continuous map between manifolds of equal dimension. In other words, we need topological… CONTINUE READING

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