Some bounds for the genus of $Mⁿ ? I$

Abstract

Starting from a $(i,j)$-symmetric crystallization $(Γ_{Mⁿ},γ_{Mⁿ})$ of a closed n-manifolds $Mⁿ$, we give an algorithm to build a crystallization $(Γ^A_{Mⁿ},γ^A_{Mⁿ})$ OF $Mⁿ? I$. This algorithm allows to give a formula for the calculation of the regular genus of $(Γ^A_{Mⁿ}, γ^A_{Mⁿ})$, in the cases $n=2,3$, and some bounds for the genus of the product-manifolds represented.