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Cubical simplicial volume

Clara Löh and Christian Plankl


Cubical simplicial volume is a variation on simplicial volume, based on cubes instead of simplices. Both invariants are homotopy invariants of oriented closed connected manifolds. In this note, we prove that cubical simplicial volume of oriented closed connected surfaces is proportional to ordinary simplicial volume. More precisely, the cubical simplicial volume of an oriented closed connected surface of genus g > 0 is equal to 2g-2.


Simplicial volume, cubical singular homology

Mathematical Subject Classification 2010

Primary: 55N10, 57N65


Received: 1st September 2015
Accepted: 31st March 2017
Published: 29th January 2019
Editor: Shmuel Weinberger