Let K be a finite, connected, abstract simplicial complex. The Morse complex of K, first introduced by Chari and Joswig, is the simplicial complex constructed from all gradient vector fields on K. We show that if K is neither the boundary of the n-simplex nor a cycle, then $\mathrm{Aut}(\mathcal{M}(K))\cong \mathrm{Aut}(K)$. In the case where $K=C_n$, a cycle of length n, we show that $\mathrm{Aut}(\mathcal{M}(C_n))\cong \mathrm{Aut}(C_{2n})$. When $K=\partial {\mathrm{\Delta }}^n$, we prove that $\mathrm{Aut}(\mathcal{M}(\partial {\mathrm{\Delta }}^n))\cong \mathrm{Aut}(\partial {\mathrm{\Delta }}^n)\times {\mathbb{Z}}_2$. These results are based on recent work of Capitelli and Minian.

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关于 Morse 复形的自同构群

设K是一个有限的、连通的、抽象的单纯复形。K的 Morse 复形，首先由 Chari 和 Joswig 引入，是由K上的所有梯度向量场构造的单纯复形。我们证明，如果K既不是n -单纯形的边界也不是环，那么$\mathrm{自动}(\mathcal{米}(钾))\cong \mathrm{自动}(钾)$. 在这种情况下$钾=C_n$，长度为n的循环，我们证明$\mathrm{自动}(\mathcal{米}(C_n))\cong \mathrm{自动}(C_{2n})$. 什么时候$钾=\partial {\mathrm{\Delta }}^n$，我们证明 $\mathrm{自动}(\mathcal{米}(\partial {\mathrm{\Delta }}^n))\cong \mathrm{自动}(\partial {\mathrm{\Delta }}^n)\times {\mathbb{Z}}_2$. 这些结果基于 Capitelli 和 Minian 最近的工作。