2-LC三角流形是指数型的

IF 1.5 Q2 PHYSICS, MATHEMATICAL
Bruno Benedetti, Marta Pavelka
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引用次数: 0

摘要

我们引入“$t$-LC三角流形”作为由$d$-简单树通过递归识别两个边界$(d-1)$面而得到的三角化,其相交至少具有$d-t-1$维数。$t$-LC概念插入到Durhuus- Jonsson引入的LC流形类(对应于$t=1$的情况)和所有流形类($t=d$的情况)之间。Benedetti—Ziegler证明了最多有$2^{d^2 \, N}$三角化的$1$-LC $d$流形具有$N$个面。本文证明了具有$N$面的$2^{\frac{d^3}{2}N}$三角化的$2$-LC $d$流形。这可以推广到所有维度这是Mogami对d=3的直觉。我们还引入了“$t$可构造复合体”,在可构造复合体(情况$t=1$)和所有复合体(情况$t=d$)之间进行插值。我们证明了所有$t$可构造伪流形都是$t$-LC,并且所有$t$可构造配合物的(同局部)深度大于$d-t$。这扩展了Hochster关于可构造复合体是(同伦)Cohen- Macaulay的著名结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
2-LC triangulated manifolds are exponentially many
We introduce"$t$-LC triangulated manifolds"as those triangulations obtainable from a tree of $d$-simplices by recursively identifying two boundary $(d-1)$-faces whose intersection has dimension at least $d-t-1$. The $t$-LC notion interpolates between the class of LC manifolds introduced by Durhuus--Jonsson (corresponding to the case $t=1$), and the class of all manifolds (case $t=d$). Benedetti--Ziegler proved that there are at most $2^{d^2 \, N}$ triangulated $1$-LC $d$-manifolds with $N$ facets. Here we prove that there are at most $2^{\frac{d^3}{2}N}$ triangulated $2$-LC $d$-manifolds with $N$ facets. This extends to all dimensions an intuition by Mogami for $d=3$. We also introduce"$t$-constructible complexes", interpolating between constructible complexes (the case $t=1$) and all complexes (case $t=d$). We show that all $t$-constructible pseudomanifolds are $t$-LC, and that all $t$-constructible complexes have (homotopical) depth larger than $d-t$. This extends the famous result by Hochster that constructible complexes are (homotopy) Cohen--Macaulay.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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