简短的新Dowker对偶性证明
Short, new proofs of Dowker duality
AI总结：
本文通过三种简短新方法证明Dowker对偶性，引入了关系连接和关系积复形，展示了 simplicial 复形与关系复形的同调在长正合列中相互关联。
摘要：
本文提出了三种简短的新证明，用于Dowker对偶性。我们引入了关系连接和关系积复形，这些复形可以在存在simplicial复形面poset之间关系的情况下构造，涵盖了Dowker对偶性和复形覆盖的上下文。在更一般的设定中，我们证明了simplicial复形和关系复形的同调在长正合列中相互关联。
英文摘要：
This paper presents three short, new proofs of Dowker duality using various poset fiber lemmas. We introduce modifications of joins and products of simplicial complexes called relational join and relational product complexes. These relational complexes can be constructed whenever there is a relation between the face posets of simplicial complexes, which includes the context of Dowker duality and covers of simplicial complexes. In this more general setting, we show that the homologies of the simplicial complexes and the relational complexes fit together in a long exact sequence.
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