A note on nontrivial intersection for selfmaps of complex Grassmann manifolds

zbMATH Open1387.55003arXiv1705.10571MaRDI QIDQ1704382

Peng Zhang

Publication date: 9 March 2018

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Abstract: Let $G(k,n)$ be the complex Grassmann manifold of $k$-planes in $mathbb{C}^{k+n}$. In this note, we show that for $1<k<n$ and for any selfmap $f:G(k,n)oG(k,n)$, there exists a $k$-plane $V^{k}inG(k,n)$ such that $f(V^k)cap{V}^{k}e0$.

Full work available at URL: https://arxiv.org/abs/1705.10571

zbMATH Keywords

fixed pointcomplex Grassmann manifold

Mathematics Subject Classification ID

Fixed points and coincidences in algebraic topology (55M20) Homology and cohomology of homogeneous spaces of Lie groups (57T15)

Related Items (1)

The self-intersections of a smooth \(n\)-manifold in \(2n\)-space

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