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
Milestones
Received: 13 November 2018
Revised: 9 September 2019
Accepted: 12 November 2019
Published: 4 February 2020

Communicated by Józef H. Przytycki
Authors
Bridget Schreiner
Department of Mathematics
University of Notre Dame
Notre Dame, IN
United States
Franjo Šarčević
Department of Mathematics
University of Sarajevo
Bosnia and Herzegovina
Ismar Volić
Department of Mathematics
Wellesley College
Wellesley, MA
United States