On degrees of maps between Grassmannians |
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Authors: | Vimala Ramani Parameswaran Sankaran |
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Affiliation: | (1) School of Mathematics, SPIC Science Foundation, 92, G. N. Chetty Road, 600017 Madras, India |
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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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Keywords: | Grassmann manifolds Brouwer degree characteristic classes |
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