Minimal simplicial spherical mappings with a given degree

Ksenia Apolonskaya; Oleg R. Musin

Paper

Minimal simplicial spherical mappings with a given degree

Abstract

This paper studies the minimal number of vertices

required in a triangulation of the

-sphere to admit a simplicial map to the boundary of a

-simplex with a given degree

. We establish upper bounds for

in dimensions

. Furthermore, we provide exact formulas for small values of

, showing that

for

and

. A key technical result is the identity

for

, which allows us to reduce higher-dimensional cases to lower-dimensional ones. The proofs involve constructive methods based on local modifications of triangulations and combinatorial arguments.