Gromov norm
In mathematics, the Gromov norm (or simplicial volume) of a compact oriented n-manifold is a norm on the homology (with real coefficients) given by minimizing the sum of the absolute values of the coefficients over all singular chains representing a cycle. The Gromov norm of the manifold is the Gromov norm of the fundamental class.[1][2]
It is named after Mikhail Gromov, who with William Thurston, proved that the Gromov norm of a finite volume hyperbolic n-manifold is proportional to the hyperbolic volume.[1] Thurston also used the Gromov norm to prove that hyperbolic volume decreases under hyperbolic Dehn surgery.[3]
References
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<references />, or <references group="..." />External links
- Simplicial volume at the Manifold Atlas.
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- ↑ 1.0 1.1 Lua error in package.lua at line 80: module 'strict' not found..
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- ↑ Benedetti & Petronio (1992), pp. 196ff.
