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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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The simplicial volume of contractible 3-manifolds
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by Giuseppe Bargagnati and Roberto Frigerio PDF
Trans. Amer. Math. Soc. 375 (2022), 3305-3323 Request permission

Abstract:

We show that the simplicial volume of a contractible $3$-manifold not homeomorphic to $\mathbb {R}^3$ is infinite. As a consequence, the Euclidean space may be characterized as the unique contractible $3$-manifold with vanishing minimal volume, or as the unique contractible $3$-manifold supporting a complete finite-volume Riemannian metric with Ricci curvature uniformly bounded from below. In contrast, we show that in every dimension $n\geq 4$ there exists a contractible $n$-manifold with vanishing simplicial volume not homeomorphic to $\mathbb {R}^n$. We also compute the spectrum of the simplicial volume of irreducible open $3$-manifolds.
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Additional Information
  • Giuseppe Bargagnati
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Italy
  • ORCID: 0000-0002-9142-6386
  • Email: g.bargagnati@studenti.unipi.it
  • Roberto Frigerio
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Italy
  • MR Author ID: 717335
  • Email: roberto.frigerio@unipi.it
  • Received by editor(s): May 28, 2021
  • Received by editor(s) in revised form: October 4, 2021
  • Published electronically: February 24, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 3305-3323
  • MSC (2020): Primary 57K10; Secondary 53C23, 57K30, 57N65
  • DOI: https://doi.org/10.1090/tran/8605
  • MathSciNet review: 4402662