Cubical simplicial volume
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
Primary: 55N10, 57N65
|Received:||1st September 2015|
|Accepted:||31st March 2017|
|Published:||29th January 2019|