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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Fake wedges
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by John R. Klein and John W. Peter PDF
Trans. Amer. Math. Soc. 366 (2014), 3771-3786 Request permission

Abstract:

A fake wedge is a diagram of spaces $K \leftarrow A\to C$ whose double mapping cylinder is contractible. The terminology stems from the special case $A = K\vee C$ with maps given by the projections. In this paper, we study the homotopy type of the moduli space $\mathcal D(K,C)$ of fake wedges on $K$ and $C$. We formulate two conjectures concerning this moduli space and verify that these conjectures hold after looping once. We show how embeddings of manifolds in Euclidean space provide a wealth of examples of non-trivial fake wedges. In an appendix, we recall discussions that the first author had with Greg Arone and Bob Thomason in early 1995 and explain how these are related to our conjectures.
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Additional Information
  • John R. Klein
  • Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
  • MR Author ID: 308817
  • Email: klein@math.wayne.edu
  • John W. Peter
  • Affiliation: Department of Mathematics, Utica College, Utica, New York 13502
  • Email: jwpeter@utica.edu
  • Received by editor(s): August 10, 2012
  • Received by editor(s) in revised form: October 26, 2012
  • Published electronically: February 6, 2014
  • Additional Notes: The first author was partially supported by the National Science Foundation
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3771-3786
  • MSC (2010): Primary 55P15, 55P40; Secondary 55P42, 55P65, 55P43
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06030-3
  • MathSciNet review: 3192617