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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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Moduli space of metrics of nonnegative sectional or positive Ricci curvature on homotopy real projective spaces
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by Anand Dessai and David González-Álvaro PDF
Trans. Amer. Math. Soc. 374 (2021), 1-33

Abstract:

We show that the moduli space of metrics of nonnegative sectional curvature on every homotopy $\mathbb {R} P^5$ has infinitely many path components. We also show that in each dimension $4k+1$ there are at least $2^{2k}$ homotopy $\mathbb {R} P^{4k+1}$’s of pairwise distinct oriented diffeomorphism type for which the moduli space of metrics of positive Ricci curvature has infinitely many path components. Examples of closed manifolds with finite fundamental group with these properties were known before only in dimensions $4k+3\geq 7$.
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Additional Information
  • Anand Dessai
  • Affiliation: Department of Mathematics, University of Fribourg, 1700 Fribourg, Switzerland
  • MR Author ID: 630872
  • Email: anand.dessai@unifr.ch
  • David González-Álvaro
  • Affiliation: Department of Mathematics, University of Fribourg, 1700 Fribourg, Switzerland
  • Address at time of publication: ETSI de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Spain
  • Email: david.gonzalez.alvaro@upm.es
  • Received by editor(s): May 21, 2019
  • Received by editor(s) in revised form: October 22, 2019
  • Published electronically: November 3, 2020
  • Additional Notes: This work was supported in part by the SNSF-Project 200021E-172469 and the DFG-Priority programme Geometry at infinity (SPP 2026). The second-named author received support from the MINECO grant MTM2017- 85934-C3-2-P
  • © Copyright 2020 \text{by the authors}
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 1-33
  • MSC (2010): Primary 53C20, 58D27, 58J28, 19K56; Secondary 19K56, 57R55, 53C27
  • DOI: https://doi.org/10.1090/tran/8044
  • MathSciNet review: 4188176