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Thu Apr 4 14:44:58 EDT 2019

## Embedding manifolds

Application domain: I have a system where the central measurement is
phase difference between two oscillators, and I need to continously
trak this difference, keeping track of "wraparound" based on a
well-known initial point.
The main insight is to keep the representation of phase "embedded" in
the representation of a quadrature signal, as opposed to flattening it
out into a single number that cannot represent the idea of rollover in
a continous way.
I think there is a generic field here: e.g. representation of Lie
groups as sets of matices.
Can this be generalized? I.e. there are more cases where
discontinuities and ambiguities are a consequence of the
representation, and not intrinsic to the problem.
Riemann surfaces come to mind as well.
http://mathworld.wolfram.com/RiemannSurface.html
https://en.wikipedia.org/wiki/Riemann_surface

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