On the Bauer--Furuta construction
On the Bauer--Furuta construction
Using the six-functor formalism for sheaves of spectra on topological spaces, we provide a novel construction of the Bauer--Furuta invariant, as well as its family version. This approach avoids the conventional arguments based on approximations by finite-dimensional subspaces, and we instead employ the Borel--Moore homology spectra relative to Fredholm maps …