Note: Combinatorial Alexander Duality—A Short and Elementary Proof
Note: Combinatorial Alexander Duality—A Short and Elementary Proof
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注意：组合亚历山大对偶性——简短而基本的证明
DOI：
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发表时间：
2007
影响因子：
0.8
通讯作者：
M. Tancer
中科院分区：
文献类型：
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作者：
A. Björner;M. Tancer
设X是具有基集V的单纯复形，定义其亚历山大对偶为单纯复形X*={σ <$V <$V <$σ <$X}。组合亚历山大对偶指出，X的第i个约化同调群同构于X的第i个约化同调群（|V|- i-3）次约化上同调群。我们给一个独立的证明，从第一原则访问一个非专家。
Let X be a simplicial complex with ground set V. Define its Alexander dual as the simplicial complex X*={σ⊆V∣V∖σ∉X}. The combinatorial Alexander duality states that the ith reduced homology group of X is isomorphic to the (|V|−i−3)th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof from first principles accessible to a nonexpert.