Timeline for Orientability of moduli space and determinant bundle of ASD operator

3 events

when toggle format	what		by	license	comment
Jun 6, 2019 at 17:26	vote	accept	Overflowian
Jun 6, 2019 at 15:21	comment	added	mme		If it helps, the way Quillen sets up the machine is to reduce to the case of surjective $A$; it's clear enough that $\Lambda^{\text{max}}(\text{ker}(A))$ is a line bundle on the space of surjective Fredholm operators. What one does next is describe a certain "stabilization operation" if I replace $A$ with $A \oplus 0: H \oplus V \to H$. Near a particular operator $A$, one chooses a subspace $J \subset H$ so that $A' = A \oplus \text{Id}: H \oplus J \to H$ is surjective, and defines $\det(A)$ to be $\det(A') \otimes \Lambda^{\text{max}}(J).$ See 20.2 of Kronheimer-Mrowka's book.
Jun 6, 2019 at 13:29	history	answered	mme	CC BY-SA 4.0