A class of naturally generalized special generic maps

TL;DR

This paper introduces a new class of generalized special generic maps, extending existing results and exploring their algebraic and differential topological properties, with implications for manifold theory.

Contribution

It proposes a novel class of generalized special generic maps and extends fundamental results on their structures and algebraic topological properties.

Findings

Introduction of a new class of generalized special generic maps

Extension of fundamental results on structures of special generic maps

Initial exploration of algebraic and differential topological properties

Abstract

Special generic maps are generalizations of Morse functions with exactly two singular points on spheres and canonical projections of unit spheres. They restrict the manifolds of the domains strongly in considerable cases and are important in algebraic topology and differential topology of manifolds of specific classes and manifolds regarded as elementary in some senses admit such maps in considerable cases. We propose a class of generalized special generic maps in our present paper and extend a fundamental result on structures and some algebraic topological properties of special generic maps by the author. Our present study will be a pioneering study on nice classes of generalized special generic maps. Studies of algebraic topological properties and differential topological ones of special generic maps have developed due to their nice structures for example.