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A streamlined proof of the convergence of the Taylor tower for embeddings in ${\mathbb R}^n$

Volume 156 / 2019

Franjo Šarčević, Ismar Volić Colloquium Mathematicum 156 (2019), 91-122 MSC: Primary 57R40; Secondary 55R80. DOI: 10.4064/cm7363-2-2018 Published online: 14 December 2018

Abstract

Manifold calculus of functors has in recent years been successfully used in the study of the topology of various spaces of embeddings of one manifold in another. Given a space of embeddings, the theory produces a Taylor tower whose purpose is to approximate this space in a suitable sense. Central to the story are deep theorems about the convergence of this tower. We provide an exposition of the convergence results in the special case of embeddings into ${\mathbb R}^n$, which has been the case of primary interest in applications. We try to use as little machinery as possible and give several improvements and restatements of existing arguments used in the proofs of the main results.

Authors

  • Franjo ŠarčevićDepartment of Mathematics
    University of Sarajevo
    Sarajevo 7100, Bosnia and Herzegovina
    e-mail
  • Ismar VolićDepartment of Mathematics
    Wellesley College
    Wellesley, MA 02481, U.S.A.
    e-mail

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