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In the previous chapter, we recalled basic definitions and properties of chain complexes and their homology. For the definition of the connection matrix, these considerations have to be extended to the case of chain complexes which are poset filtered. In addition, we need to study maps between these poset filtered chain complexes, even in the situation where the filtration posets of the involved chain complexes differ. All of these concepts will be introduced in the current chapter.

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Poset Filtered Chain Complexes

  • 章节

  • 发表日期：

    2025年

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  • Marian Mrozek,
  • Thomas Wanner

摘要

In the previous chapter, we recalled basic definitions and properties of chain complexes and their homology. For the definition of the connection matrix, these considerations have to be extended to the case of chain complexes which are poset filtered. In addition, we need to study maps between these poset filtered chain complexes, even in the situation where the filtration posets of the involved chain complexes differ. All of these concepts will be introduced in the current chapter.