Editing Homotopy (section)

=== Timelike homotopy ===
On a [[Lorentzian manifold]], certain curves are distinguished as [[timelike]] (representing something that only goes forwards, not backwards, in time, in every local frame). A [[timelike homotopy]] between two [[timelike curve]]s is a homotopy such that the curve remains timelike during the continuous transformation from one curve to another. No [[closed timelike curve]] (CTC) on a Lorentzian manifold is timelike homotopic to a point (that is, null timelike homotopic); such a manifold is therefore said to be [[multiply connected]] by timelike curves. A manifold such as the [[3-sphere]] can be [[simply connected]] (by any type of curve), and yet be [[timelike multiply connected]].<ref>{{Cite journal|last=Monroe|first=Hunter|date=2008-11-01|title=Are Causality Violations Undesirable?|journal=Foundations of Physics|language=en|volume=38|issue=11|pages=1065–1069|doi=10.1007/s10701-008-9254-9|issn=0015-9018|arxiv=gr-qc/0609054|bibcode=2008FoPh...38.1065M|s2cid=119707350 }}</ref>