Power operations in the Stolz–Teichner program

The Stolz--Teichner program proposes a deep connection between geometric field theories and certain cohomology theories. In this paper, we extend by developing theory of power operations for restricted to closed bordisms. These satisfy relations analogous the ones exhibited their homotopical counterparts. We also provide computational tools identify geometrically defined with usual on complexified equivariant $K$-theory. Further, use approach construct elliptic cohomology.