Simplicial volume
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1 Definition and history
Definition 1.1. Let be an oriented closed connected manifold of dimension . Then the simplicial volume (also called Gromov norm) of is defined as
Here, denotes the singular chain complex of with real coefficients, and denotes the -norm on the singular chain complex induced from the (unordered) basis given by all singular simplices; i.e., for a chain (in reduced form), the -norm of is given by
2 References
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