Low stages of the Taylor tower for $r$-immersions

Bridget Schreiner; Franjo Šarčević; Ismar Volić

doi:10.2140/involve.2020.13.51

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.

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Bridget Schreiner. Franjo Šarčević. Ismar Volić. "Low stages of the Taylor tower for $r$-immersions." Involve 13 (1) 51 - 75, 2020. https://doi.org/10.2140/involve.2020.13.51

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Received: 13 November 2018; Revised: 9 September 2019; Accepted: 12 November 2019; Published: 2020

First available in Project Euclid: 20 March 2020

zbMATH: 07172111

MathSciNet: MR4059941

Digital Object Identifier: 10.2140/involve.2020.13.51

Subjects:

Primary: 57R42

Secondary: 55R80 , 57R40

Keywords: $r$-immersions , calculus of functors , configuration space , embeddings , immersions , Manifold calculus , subspace arrangement , Taylor tower

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