Constant curvature hyperspheres and the Euler Characteristic

TL;DR

This paper explores the relationship between the algebraic count of immersed hyperspheres with constant curvature and the Euler Characteristic of the ambient space, providing new insights into geometric topology.

Contribution

It establishes a connection between the algebraic number of constant curvature hyperspheres and the Euler Characteristic, offering a novel perspective in geometric topology.

Findings

Relation between algebraic count of hyperspheres and Euler Characteristic

Applicable to many cases of immersed hyperspheres

Provides new tools for studying curvature and topology

Abstract

We show how in many cases the algebraic number of immersed hyperspheres of constant (and prescribed) curvature may be related to the Euler Characteristic of the ambient space.