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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Blakers-Massey elements and exotic diffeomorphisms of $S^6$ and $S^{14}$ via geodesics
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by C. E. Durán, A. Mendoza and A. Rigas PDF
Trans. Amer. Math. Soc. 356 (2004), 5025-5043 Request permission

Abstract:

We use the geometry of the geodesics of a certain left-invariant metric on the Lie group $Sp(2)$ to find explicit related formulas for two topological objects: the Blakers-Massey element (a generator of $\pi _6(S^3)$) and an exotic (i.e. not isotopic to the identity) diffeomorphism of $S^6$ (C. E. Durán, 2001). These formulas depend on two quaternions and their conjugates and we produce their extensions to the octonions through formulas for a generator of $\pi _{14}(S^{7})$ and exotic diffeomorphisms of $S^{14}$, thus giving explicit gluing maps for half of the 15-dimensional exotic spheres expressed as the union of two 15-disks.
References
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Additional Information
  • C. E. Durán
  • Affiliation: Departamento de Matemáticas, Instituto Venezolano de Investigaciones Científicas, Apartado 21827, Caracas 1020A, Venezuela
  • Address at time of publication: IMECC-UNICAMP, C.P. 6065, 13083-970, Campinas, SP, Brazil
  • Email: cduran@cauchy.ivic.ve, cduran@ime.unicamp.br
  • A. Mendoza
  • Affiliation: Departamento de Matemáticas Puras y Aplicadas, Universidad Simón Bolívar, Apartado 28000, Caracas 1080, Venezuela
  • Email: jacob@usb.ve
  • A. Rigas
  • Affiliation: IMECC-UNICAMP, c.p. 6065, 13083-970, Campinas, SP, Brazil
  • Email: rigas@ime.unicamp.br
  • Received by editor(s): March 21, 2003
  • Received by editor(s) in revised form: July 29, 2003
  • Published electronically: June 29, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 5025-5043
  • MSC (1991): Primary 53C22; Secondary 58F07, 57R15
  • DOI: https://doi.org/10.1090/S0002-9947-04-03469-5
  • MathSciNet review: 2084409