On Nonlinear Part of Filled-Section in Splicing

TL;DR

This paper introduces a new nonlinear filled section in Gromov-Witten theory within Banach analysis, establishing its differentiability class as $C^1$, which advances the mathematical framework of the theory.

Contribution

It defines a nonlinear part of a filled section in Gromov-Witten theory using Banach analysis and proves its $C^1$ regularity, providing a new analytical approach.

Findings

The filled section is of class $C^1$.

The approach uses Banach analysis instead of polyfold theory.

Provides a foundation for further analytical developments in Gromov-Witten theory.

Abstract

We define the nonlinear part of a new filled section for Gromov-Witten theory in the setting of the usual Banach analysis rather than of ployfold theory and prove that the filled-section so defined is of class $C^1$.