Topology of boundary special generic maps into Euclidean spaces

TL;DR

This paper introduces boundary special generic maps from manifolds with boundary to Euclidean spaces, analyzing their topological restrictions and applying results to non-singular extension problems.

Contribution

It defines boundary special generic maps and explores their implications for the global structure of manifolds and extension of maps.

Findings

Derived topological restrictions for manifolds admitting such maps

Established conditions for non-singular extensions of special generic maps

Provided new insights into the structure of boundary maps and extensions

Abstract

We introduce boundary special generic maps, a class of submersions from manifolds with boundary to Euclidean spaces whose restriction to the boundary has only boundary definite fold points as its singular points. We derive the differential-topological restrictions imposed by the existence of such maps on the global structure of the source manifolds. Furthermore, we apply our results to the non-singular extension problem, which asks when a map on a closed manifold extends to a non-singular map on a manifold with boundary, and obtain new results on non-singular extensions of special generic maps.