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We introduce and study a combinatorially defined notion of root basis of a (real) root system of a possibly infinite Coxeter group. Known results on conjugacy up to sign of root bases of certain irred...
Rigidity of Graph Joins and Hendrickson's Conjecture
Graph Joins Hendrickson's Conjecture
2010/11/19
Whiteley gives a complete characterization of the infinitesimal flexes of complete bipartite frameworks. Our work generalizes a specific infinitesimal flex to include joined graphs, a family of graphs...
We prove that for a finite or profinite group G, the homotopy infor-mation of rational G-pectra is entirely determined by the triangulated structure of their homotopy category.
Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere
principal curvature Clifford torus Gauss equations
2007/12/12
In this paper, we give a characterization of tori $S^1\left(\sqrt{\frac{nr+2-n}{nr}}\right)\times S^{n-1}\left(\sqrt{\frac{n-2}{nr}}\right)$ and $S^m\left(\sqrt{\frac{m}{n}}\right)\times S^{n-m}\left(...
We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a fa...