论文标题
Sigma-Invariants和Tropical品种
Sigma-invariants and tropical varieties
论文作者
论文摘要
bieri-neumann-strebel-renz不变式$σ^q（x，x，\ mathbb {z}）\ subset h^1（x，x，x，\ mathbb {r}）$的有限型CW-Complex $ x $是Novikov-Sikov-Sikorav的消失范围，杂志$ Q $ $ \ MATHCAL {V}^q（x）\子集h^1（x，x，\ mathbb {c}^{\ times}）$是与$ q $等级1本地系统中系数的同源性的非趋化位点。我们表明，每个BNSR不变$σ^q（x，\ mathbb {z}）$包含在与代数品种$ \ Mathcal {v}^{\ le q}（\ le q}（x）$相关的热带品种的补充中，并为几个类别和空间提供应用程序。
The Bieri-Neumann-Strebel-Renz invariants $Σ^q(X,\mathbb{Z})\subset H^1(X,\mathbb{R})$ of a connected, finite-type CW-complex $X$ are the vanishing loci for Novikov-Sikorav homology in degrees up to $q$, while the characteristic varieties $\mathcal{V}^q(X) \subset H^1(X,\mathbb{C}^{\times})$ are the nonvanishing loci for homology with coefficients in rank 1 local systems in degree $q$. We show that each BNSR invariant $Σ^q(X,\mathbb{Z})$ is contained in the complement of the tropical variety associated to the algebraic variety $\mathcal{V}^{\le q}(X)$, and provide applications to several classes of groups and spaces.
