$C^{m_0}$-Smoothness of Evaluation Maps

TL;DR

This paper proves that the evaluation map in a certain mathematical setting is of class $C^{m_0}$, establishing its smoothness properties.

Contribution

It provides a proof that the evaluation map $E$ is of class $C^{m_0}$, clarifying its smoothness in the context of differential geometry.

Findings

Evaluation map $E$ is of class $C^{m_0}$.

The proof confirms the smoothness level of $E$ in the specified setting.

Supports further analysis of smooth structures in related geometric contexts.

Abstract

We give a proof that evaluation map $E: \Sigma^l\times {\cal M}\rightarrow M^l$ is of class $C^{m_0}$.