  We relate physical time with the topology of magnetic field vortices. We base
ourselves on a formulation of unimodular gravity where the cosmological
constant $\Lambda$ appears as the canonical dual to a variable which on-shell
becomes four-volume time. If the theory is restricted to a topological axionic
form (viz. a parity-odd product of an electric and a magnetic field), such a
time variable becomes the spatial integral of the Chern-Simons density. The
latter equates to helicity, so that unimodular time is transmuted into the
linking number of the vortices of the topological magnetic field, times their
flux. With the added {\it postulate} that this flux is a universal constant,
the flow of time can thus be interpreted as the progressive weaving of further
links between magnetic field vortices, each link providing a quantum of time
with value related to the fixed flux. Non-abelian extensions, and targetting
parameters other than $\Lambda$ are briefly examined, exposing different types
of vortices and a possible role for inter-linking leading to new phenomenology.
