The homotopy classification and the index of boundary value problems for general elliptic operators

TL;DR

This paper develops a homotopy classification and computes the index for boundary value problems involving general elliptic operators, extending classical results to more general cases beyond Atiyah-Bott conditions.

Contribution

It introduces a homotopy classification framework and index computation method for elliptic boundary value problems without the Atiyah-Bott condition.

Findings

Classical Atiyah-Bott case analyzed in detail

Extension to non-Atiyah-Bott elliptic operators achieved

Provides a new classification and index formula for general elliptic boundary problems

Abstract

We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.