## 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