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In this chapter, we collect background material that is necessary for the more technical parts of the book. This includes both definitions and fundamental results. We begin with a discussion of relations and partial orders, before moving on to topological spaces. The following two sections are more algebraic in nature, as they address modules, chain complexes, and homology. Finally, the last section is concerned with a detailed survey of Lefschetz complexes.

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Algebraic and Topological Background Material

  • 章节

  • 发表日期：

    2025年

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  • Marian Mrozek,
  • Thomas Wanner

摘要

In this chapter, we collect background material that is necessary for the more technical parts of the book. This includes both definitions and fundamental results. We begin with a discussion of relations and partial orders, before moving on to topological spaces. The following two sections are more algebraic in nature, as they address modules, chain complexes, and homology. Finally, the last section is concerned with a detailed survey of Lefschetz complexes.