Semi-Fredholmness on a weighted geometric realization of ۲-simplexes and ۳- simplexes

In this present article, we introduce the notion of oriented ۲-simplexes and the notion of oriented ۳-simplexes and we use them to create a new framework that we call a weighted geometric realization of ۲-simplexes and ۳-simplexes. Next, we define the weighted geometric realization Gauss-Bonnet operator L. After that, we present and study the non-parabolicity at the infinity of  L. Finally, we develop general conditions to ensure semi-Fredholmness of L based on its non-parabolicity at infinity.

Keywords:

Weighted geometric realization of ۲-simplexes and ۳-simplexes , weighted geometric realization Gauss-Bonnet operator , non-parabolicity at infinity , semi-Fredholmness