Calabi-Yau

Calabi-Yau manifolds are compact Kähler manifolds
whose canonical bundle is trivial.

In superstring theory the extra dimensions of spacetime
may take the form of a 6-dimensional Calabi–Yau manifold.

‎”Canonical bundle” is just another name for “invertible sheaf.”

An invertible sheaf is exactly like a line bundle, only
transposed from topology into algebraic geometry.

Real line bundles are double covers of differential manifolds,
and now we arrive at a relatively familiar example:

A Mobius strip is a double cover of a circle!

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