About: Trigenus

In low-dimensional topology, the trigenus of a closed 3-manifold is an invariant consisting of an ordered triple . It is obtained by minimizing the genera of three orientable handle bodies — with no intersection between their interiors— which decompose the manifold as far as the Heegaard genus need only two. That is, a decomposition withfor and being the genus of . For orientable spaces, ,where is 's Heegaard genus. For non-orientable spaces the has the form depending on theimage of the first Stiefel–Whitney characteristic class under a Bockstein homomorphism, respectively for