It is shown that there are restrictions on the possible changes of topology of space sections of the universe if this topology change takes place in a compact region which has a Lorentzian metric and spinor structure. In particular, it is impossible to create a single wormhole or attach a single handle to a spacetime but it is kinematically possible to create such wormholes in pairs. Another way of saying this is that there is a ℤ2 invariant for a closed oriented 3-manifold Σ which determines whether Σ can be the spacelike boundary of a compact manifoldM which admits a Lorentzian metric and a spinor structure. We evaluate this invariant in terms of the homology groups of Σ and find that it is the mod2 Kervaire semi-characteristic.

/pdf/selection-rules-for-topology-change-3bxkcak99m.pdf

Selection rules for topology change

Lorentz gauge invariant vacuum functionals for quantized spinor fields in non-simply connected space-times

We discuss various methods for investigating the existence and uniqueness of generalized spin structures. We show that on a four dimensional manifold whole families may be constructed using any internal symmetry group of the formG/ℤ2, whereG is a simply connected Lie group.

/pdf/generalized-spin-structures-on-four-dimensional-space-times-5efol1ef5e.pdf

Generalized spin structures on four dimensional space-times

Generalized Spin Structures on Four Dimensional Spacetimes

An explicit construction of spinor structures on real, complex, and quaternionic projective spaces is given for all cases when they exist The construction is based on a theorem describing the bundle of orthonormal frames of a homogeneous Riemannian manifold This research is motivated by a remarkable coincidence of spinor connections on low‐dimensional spheres with simple, topologically nontrivial gauge configurations

Spinor structures on spheres and projective spaces

Universal classifying spaces and characteristic classes for O(p,q)-bundles are constructed and applied in the case (p,q) =(1,3) to the Lorentz bundle of a relativistic spacetime. The classes are used to investigate the existence of Uspinor structure on space and time orientable spacetimes, and spinor structures on nonorientable spacetimes.

Lorentzian characteristic classes

The paper is divided into two parts. The first part is a detailed review of the topological background to the theory of spinor structures on space-times, including proofs of most of the main results. The second part is a contination of the analysis in the second paper of this series of the cobordism theory of compact, closed, orientable space-time manifolds. A new cobordism relation is defined: linear spin cobordism and the linear spin cobordism of space-time manifolds calculated.

Topics on space-time topology (III)

The topological and geometrical restrictions on spatially integrable space-times foliated by space-like hypersurfaces are investigated.

Spatially integrable space--times

It is demonstrated that a compact space and time-orientable space-time is cobordant in the unoriented sense, that is, bounds a compact five-manifold. The bounding property is a direct consequence of the triviality of the Euler number.

‘Hyperspace’ (the cobordism theory of space-time)

Several topics in the geometry of space-times are discussed, including the time and space-distributions of the space-time and a geometrical definition of singularities.

George S. Whiston

Papers

Lorentzian characteristic classes

Topics on space-time topology (III)

Spatially integrable space--times

‘Hyperspace’ (the cobordism theory of space-time)

Topics on space-time geometry