Timelike homotopy
On a Lorentzian manifold, certain curves are distinguished as timelike. A timelike homotopy between two timelike curves is a homotopy such that each intermediate curve is timelike. No closed timelike curve on a Lorentzian manifold is timelike homotopic to a point ; such a manifold is therefore said to be multiply connected by timelike curves. A manifold such as the 3-sphere can be simply connected, and at the same time be timelike multiply connected. Equivalence classes of timelike homotopic curves define their own fundamental group, as noted by Smith. A smooth topological feature which prevents a CTC from being deformed to a point may be called a timelike topological feature.
