A note on the characteristic rank of oriented Grassmann manifolds

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• 作者：Tomá ; &scaron ; Rusin ^{svmydlo@gmail.com}
• 关键词：57R20 ; 55R25
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：216
• 期：Complete
• 页码：48-58
• 全文大小：314 K
• 卷排序：216

文摘

We derive new lower bound for the characteristic rank of the canonical 3-plane bundle γ˜n,3 over the oriented Grassmann manifold G˜n,3≅SO(n)/(SO(3)×SO(n−3)) for all n   in range 2t+2t−1≤n≤2t+1−42t+2t−1≤n≤2t+1−4, t≥3t≥3. Using this knowledge we determine the Z2Z2-cup-length of G˜2t+2t−1+1,3 and G˜2t+2t−1+2,3, verifying the corresponding claim of T. Fukaya's conjecture.