2021/11/15 by Jack Morava, Morava, Jack
Mathematics · #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2111.08053
The Cayley transform compactifies Minkowski space \M, realized as self-adjoint 2×2 complex matrices following Penrose, as the unitary group \U(2). Its complement is a compactification of a copy of a light-cone as it is usually drawn, constructed by adjoining a bubble or \CP1 of unitary matrices with eigenvalue ± 1 at the ends of a lightcone at infinity. The Brauer-Wall group of \U(2) (i.e. of fields of certain kinds of graded \Cs-algebras, up to projective equivalence) is \Z2 × \Z, defining an interesting class of nontrivial examples of Araki-Haag-Kastler backgrounds for quantum field theories on compactified Minkowski space. The second part of this paper extends such models to link presentations of more general spin four-manifolds.