New inverse and implicit function theorems for differentiable maps with isolated critical points

2021/04/01 by Liangpan Li, Li, Liangpan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2104.00371

openalex publication_date 2021/04/01 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28

Abstract

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with isolated critical points are discrete maps, which means that algebraic topology methods could then be deployed to explore relevant questions. We also provide a purely topological version of implicit function theorem for continuous maps that still possesses unique existence and continuity. All new results of the paper are optimal with respect to the choice of dimensions.

Citations

• A General Implicit/Inverse Function Theorem

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