Shtrezi, Orion
(2026)
Topology-induced structure and local-to-global symmetry.
[Preprint]
Abstract
Grimmer and Read argue that certain flat but almost/asymmetric spatial topologies, espe-
cially the Hantzsche–Wendt manifold, affect two questions in the philosophy of spacetime: the
equivalence of spacetime theories and the determinism of those theories. On fixed Hantzsche–
Wendt product backgrounds, several familiar distinctions between global automorphism groups
collapse, even though the corresponding structures remain locally distinct. This paper gives a
sheaf-theoretic way of keeping these two facts separate. The first calculation is that, for any
compact connected flat spatial manifold Σ, the Killing sheaf of the static Lorentzian product
(R × Σ, −dt2 + h) has global sections
H0(R × Σ, K) ∼= R ⊕ H0(Σ, Kh).
Thus the Hantzsche–Wendt product has Poincaréan Killing-sheaf stalks but only the time-
translation Killing field globally. The second calculation treats the rigging sector of the New-
tonian/Leibnizian comparison as a torsor under vertical metric-preserving fields; in the static
Hantzsche–Wendt case this torsor has a unique global section. Finally, the determinism definitions
used by Grimmer and Read are written as extension and uniqueness conditions for restriction
maps from full isometries to isometries of initial segments. The aim is not to replace their global
automorphism-group analysis, but to record the local automorphism data that such an analysis
suppresses.
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