Shifted Symplectic Structures on Spaces of Framed Maps

This work examines the existence of shifted symplectic and Poisson structures on certain spaces of framed maps. We define n-shifted Poisson structures and coisotropic structures in terms of shifted symplectic structures and Lagrangian structures. Shifted Poisson structures are shown to have properties analogous to those of shifted symplectic structures, and reduce to ordinary Poisson structures in the classical case. Next, we examine the space Map(X,D,Y) of maps from X to Y, framed along some divisor D. These are shown to inherit a shifted symplectic or Poisson structure from Y in certain conditions. This construction is used to rederive the existence of symplectic and Poisson structures in classical examples.