Low stages of the Taylor tower for r-immersions

TL;DR

This paper investigates the initial layers of the Taylor tower in manifold calculus for r-immersions, providing detailed descriptions and connectivity results, advancing understanding of immersions without r-fold self-intersections.

Contribution

It describes the first r layers of the Taylor tower for r-immersions and analyzes the connectivities of the related maps, offering new insights into the structure of r-immersions.

Findings

Explicit description of the first r layers of the Taylor tower

Connectivity results for the associated maps

Independent results on properties of r-immersions

Abstract

We study the beginning of the Taylor tower, supplied by manifold calculus of functors, for the space of r-immersions, which are immersions without r-fold self-intersections. We describe the first r layers of the tower and discuss the connectivities of the associated maps. We also prove several results about r-immersions that are of independent interest.