Semi-Fredholmness on a weighted geometric realization of 2-simplexes and 3- simplexes
نویسندگان
1 Laboratoire de Mathematiques Fondamentales et Appliquees, Departement de Mathematiques et Informatique, Faculte des Sciences Ain Chock, Universite Hassan II de Casablanca, Morocco
2 Laboratoire de Mathematiques Fondamentales et Appliquees, Faculte des Sciences Ain Chock, Universite Hassan II de Casablanca, Morocco
doi
10.22075/ijnaa.2023.26602.3363چکیده
In this present article, we introduce the notion of oriented $2$-simplexes and the notion of oriented $3$-simplexes and we use them to create a new framework that we call a weighted geometric realization of $2$-simplexes and $3$-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.
