  We construct a Chern-Simons gauge theory for dg Lie and L-infinity algebras
on any one-dimensional manifold and quantize this theory using the
Batalin-Vilkovisky formalism and Costello's renormalization techniques. Koszul
duality and derived geometry allow us to encode topological quantum mechanics,
a nonlinear sigma model of maps from a 1-manifold into a cotangent bundle T*X,
as such a Chern-Simons theory. Our main result is that the partition function
of this theory is naturally identified with the A-genus of X. From the
perspective of derived geometry, our quantization construct a volume form on
the derived loop space which can be identified with the A-class.
