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On degrees of maps between Grassmannians

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Abstract

Let Gn,k denote the oriented grassmann manifold of orientedk-planes in ℝn. It is shown that for any continuous mapf: Gn,k → Gn,k, dim Gn,k = dim Gm,l = l(m −l), the Brouwer’s degree is zero, providedl > 1,n ≠ m. Similar results for continuous mapsg: ℂGm,l → ℂGn,k,h: ℍGm,l → ℍGn,k, 1 ≤ l < k ≤ n/2, k(n — k) = l(m — l) are also obtained.

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Authors and Affiliations

  1. School of Mathematics, SPIC Science Foundation, 92, G. N. Chetty Road, 600017, Madras, India

    Vimala Ramani & Parameswaran Sankaran

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  1. Vimala Ramani
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  2. Parameswaran Sankaran
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Ramani, V., Sankaran, P. On degrees of maps between Grassmannians. Proc. Indian Acad. Sci. (Math. Sci.) 107, 13–19 (1997). https://doi.org/10.1007/BF02840469

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  • DOI: https://doi.org/10.1007/BF02840469

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