Homology

Edwin H. Spanier
Additional contact information
Edwin H. Spanier: University of California, Department of Mathematics

Chapter Chapter Four in Algebraic Topology, 1966, pp 154-209 from Springer

Abstract: Abstract this chapter introduces the concept of homology theory, which is of fundamental importance in algebraic topology. A homology theory involves a sequence of covariant functors H n to the category of abelian groups, and we shall define homology theories on two categories-the singular homology theory on the category of topological pairs and the simplicial homology theory on the category of simplicial pairs. The former is topologically invariant by definition and is formally easier to work with, while the latter is easier to visualize geometrically and by definition is effectively computable for finite simplicial complexes. The two theories are related by the basic result that the singular homology of a polyhedron is isomorphic to the simplicial homology of any of its triangulating simplicial complexes.

Keywords: Exact Sequence; Simplicial Complex; Chain Complex; Homology Group; Short Exact Sequence (search for similar items in EconPapers)
Date: 1966
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4684-9322-1_5

Ordering information: This item can be ordered from
http://www.springer.com/9781468493221

DOI: 10.1007/978-1-4684-9322-1_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().