In the mathematical field of geometric topology, the simplicial volume (also called Gromov norm) is a measure of the topological complexity of a manifold.
More generally, the simplicial norm measures the complexity of homology classes.
Given a closed and oriented manifold, one defines the simplicial norm by minimizing the sum of the absolute values of the coefficients over all singular chains homologous to a given cycle.
[1] The simplicial volume is equal to twice the Thurston norm.
[3] Thurston also used the simplicial volume to prove that hyperbolic volume decreases under hyperbolic Dehn surgery.