Callias

Callias refers to a class of operators in mathematical analysis, particularly in the study of differential operators on manifolds. Named after mathematician Paul Callias, these operators are characterized by having special "admissible" properties at infinity, allowing them to be analyzed using techniques similar to those used for compact operators. They are important in index theory and noncommutative geometry because they enable the extension of analytical tools to non-compact spaces, facilitating the calculation of invariants that classify geometric and topological features of manifolds.