#### Vol. 13, No. 1, 2020

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

### Bridget Schreiner, Franjo Šarčević and Ismar Volić

Vol. 13 (2020), No. 1, 51–75
##### 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.

##### Keywords
calculus of functors, manifold calculus, Taylor tower, $r$-immersions, embeddings, immersions, configuration space, subspace arrangement
##### Mathematical Subject Classification 2010
Primary: 57R42
Secondary: 55R80, 57R40