A Note on the Penrose–Mackay Tiling, HirzbruchSignature of M 4 and Knots in e (∞) Space

Mackays generalization of Penrose tiling is shown to be related to the Hirzbruchsignature, δ, of four manifolds in the case of a Murray–von Neumann continuousdimension in E (∞) space. It is further shown that σ is numerically identicalto the Jones knot invariant, VL, for the right-handed trefoil. Finally, aconjecture regarding the theorem of local isomorphism is presented.