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4-Manifold topology I: Subexponential groups

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Abstract

The technical lemma underlying the 5-dimensional topologicals-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating π1-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (“good groups”) where the π1-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92093-0112, San Diego, La Jolla, CA, USA

    Michael H. Freedman

  2. Fachbereich Mathematik, Universität Mainz, D-55099, Mainz, Germany

    Peter Teichner

Authors
  1. Michael H. Freedman
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  2. Peter Teichner
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Oblatum 20-II-1995 & 26-V-1995

The first author is supported by the IHES, the Guggenheim foundation and the NSF.

The second author is supported by the IHES and the Humboldt foundation.

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Freedman, M.H., Teichner, P. 4-Manifold topology I: Subexponential groups. Invent Math 122, 509–529 (1995). https://doi.org/10.1007/BF01231454

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