Mayer-Vietoris sequence
Let is a topological space, and are such that , and . Then there is an exact sequence of homology groups:
Here, is induced by the inclusions and by , and is the following map: if is in , then it can be written as the sum of a chain in and one in , . , since . Thus, is a chain in , and so represents a class in . This is . One can easily check (by standard diagram chasing) that this map is well defined on the level of homology.
Title | Mayer-Vietoris sequence |
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Canonical name | MayerVietorisSequence |
Date of creation | 2013-03-22 13:14:52 |
Last modified on | 2013-03-22 13:14:52 |
Owner | bwebste (988) |
Last modified by | bwebste (988) |
Numerical id | 6 |
Author | bwebste (988) |
Entry type | Definition |
Classification | msc 55N10 |