The paper proposes a rational homotopy model for a classifying space of locally conformally symplectic four-manifolds and a cobordism category of three-manifolds with Omega^2 S^2-bundle framings, but the standalone text does not prove the construction.
At the boundary of Minkowski space
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abstract
The Cayley transform compactifies Minkowski space $\M$, realized as self-adjoint $2\times2$ 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 $\CP_1$ of unitary matrices with eigenvalue $\pm 1$ 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 $\Z_2 \times \Z$, 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.
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Boundary framings for locally conformally symplectic four-manifolds
The paper proposes a rational homotopy model for a classifying space of locally conformally symplectic four-manifolds and a cobordism category of three-manifolds with Omega^2 S^2-bundle framings, but the standalone text does not prove the construction.