A stable cohomotopy refinement of Seiberg-Witten invariants: I
  The monopole map defines an element in an equivariant stable cohomotopy group refining the Seiberg-Witten invariant. This first of two articles presents the details of the definition of the stable cohomotopy invariant and discusses its relation to the integer valued Seiberg-Witten invariant. 
Stefan Bauer and Mikio Furuta