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- W2794466774 abstract "An arrow matrix is a matrix with zeroes outside the main diagonal, first row, and first column. We consider the space $M_{St_n,lambda}$ of Hermitian arrow $(n+1)times (n+1)$-matrices with fixed simple spectrum $lambda$. We prove that this space is a smooth $2n$-manifold, and its smooth structure is independent on the spectrum. Next, this manifold carries the locally standard torus action: we describe the topology and combinatorics of its orbit space. If $ngeqslant 3$, the orbit space $M_{St_n,lambda}/T^n$ is not a polytope, hence this manifold is not quasitoric. However, there is a natural permutation action on $M_{St_n,lambda}$ which induces the combined action of a semidirect product $T^nrtimesSigma_n$. The orbit space of this large action is a simple polytope. The structure of this polytope is described in the paper. In case $n=3$, the space $M_{St_3,lambda}/T^3$ is a solid torus with boundary subdivided into hexagons in a regular way. This description allows to compute the cohomology ring and equivariant cohomology ring of the 6-dimensional manifold $M_{St_3,lambda}$ using the general theory developed by the first author. This theory is also applied to a certain $6$-dimensional manifold called the twin of $M_{St_3,lambda}$. The twin carries a half-dimensional torus action and has nontrivial tangent and normal bundles." @default.
- W2794466774 created "2018-04-06" @default.
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- W2794466774 date "2018-03-28" @default.
- W2794466774 modified "2023-09-27" @default.
- W2794466774 title "Manifolds of isospectral arrow matrices" @default.
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