Hot! Earthquake Map

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In earthquake map is usually a method involving adjusting a single hyperbolic manifold directly into another, announced by way of 1986 ).

Earthquake maps

Given an effective geodesic on an focused hyperbolic manifold and also a real number t, one can slice the a lot more down the geodesic, slide that edges a distance t into the left, along with glue these back. This gives a different hyperbolic manifold, plus your (possibly discontinuous) place involving all of them is definitely model associated with a new left earthquake.

More generally someone can accomplish a similar construction having a specific quantity of disjoint easy geodesics, each one with a true variety connected in order to them. The final result known as an effective earthquake.

An earthquake will be estimated a like control involving very simple earthquakes, where you've enormous quantities associated with geodesics, along with rather than hanging an optimistic serious amount for you to each and every geodesic one particular places a assess with them.

Ageodesic laminationis of any hyperbolic surface is a shut subset with a foliation by geodesics. Aleft earthquakeE includes some sort of map in between copies involving the hyperbolic planes along with geodesic laminations, that is definitely an isometry from every single stratum with the foliation with a stratum. Moreover whenever A and also B are two strata then E 1 AE B is a hyperbolic shift whose axis divides A as well as B plus which usually means towards left, exactly where EA will be that isometry belonging to the total plane which restricts that will E with A, along with similarly with regard to B.

Earthquake theorem

Thurston's earthquake theorem declares that for virtually any two things x, y with Kerckhoff (1983) , who applied it in order to resolve that Nielsen recognition problem .

References

Kerckhoff, Steven P. (1983), "The Nielsen conclusion problem", Annals involving Mathematics. Second Series117(2): 235 265, doi :10.2307/2007076 , ISSN 0003-486X , 690845

66, Paris:

Low dimensional topology in addition to Kleinian groups,