Hot! Earthquake Map

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In earthquake guide is usually a procedure for changing a single hyperbolic manifold straight into another, announced by way of 1986 ).

Earthquake maps

Given a uncomplicated geodesic about a strong oriented hyperbolic a lot more as well as a real number t, you can reduce your manifold under the geodesic, fall the moves a mileage t to the left, and glue them back. This provides a different hyperbolic manifold, and also the (possibly discontinuous) road in between them is usually an model of an left earthquake .

More generally one can perform similar building by using some sort of specific quantity of disjoint uncomplicated geodesics, just about every together with a genuine quantity along with them. The consequence known as an effective earthquake .

An earthquake can be roughly a almost restriction regarding simple earthquakes, where one has thousands regarding geodesics, and rather involving affixing a optimistic real range in order to every geodesic one puts some sort of calculate upon them.

Ageodesic laminationis of an hyperbolic outside is a closed subset that has a foliation through geodesics. Aleft earthquakeE features a road in between copies in the hyperbolic plane with geodesic laminations, that will is usually an isometry coming from every single stratum from the foliation for you to some sort of stratum. Moreover when A in addition to B are usually a couple of strata next E 1 AE B will be your hyperbolic transformation whose axis sets apart A plus B along with which means to help this left, where EA will be isometry of the whole plane that confines to E upon A, as well as likewise with regard to B.

Earthquake theorem

Thurston's earthquake theorem states of which for almost any a pair of items x, y involving Kerckhoff (1983) , which made use of them to resolve that Nielsen realization problem .

References

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

66, Paris:

Low dimensional topology and Kleinian groups,