On the Index of Elliptic Operators on Manifolds with Cylindrical Ends

Key Points

• The aim is to derive an index formula for elliptic operators on manifolds with cylindrical ends, specifically when the cylinder's base is a torus.
• Developed a new local algebraic index theorem for families of elliptic symbols.
• Utilized surgery techniques on elliptic operators.
• Established an index formula applicable to elliptic operators on the defined manifolds.
• Provided a rigorous proof rooted in the newly developed algebraic index theorem.