Hot! Earthquake Map

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In earthquake place is a way connected with changing a single hyperbolic manifold into another, launched by means of 1986 ).

Earthquake maps

Given an easy geodesic on a great focused hyperbolic manifold plus a actual selection t, one can minimize this a lot more together your geodesic, slip your edges a mileage capital t into the left, and glue them back. This gives a innovative hyperbolic manifold, plus the actual (possibly discontinuous) place between these individuals is usually an case in point on the quit earthquake.

More normally anybody can carry out the same design which has a finite quantity of disjoint uncomplicated geodesics, each one having a actual variety attached with them. The final result is called a simple earthquake.

An earthquake will be about some sort of almost limit of simple earthquakes, wherever one particular features thousands of geodesics, plus instead of hanging some sort of constructive actual number to help each geodesic one particular sets some sort of calculate upon them.

Ageodesic laminationis of the hyperbolic surface area is definitely some sort of shut down subset which includes a foliation by means of geodesics. Aleft earthquakeE is made of a guide between copies on the hyperbolic plane using geodesic laminations, that may be an isometry from every stratum on the foliation into a stratum. Moreover whenever A in addition to B are a pair of strata after that E just one AE B can be a hyperbolic alteration whose axis separates A plus B and which in turn means towards the left, where EA is your isometry belonging to the complete aeroplanes that restricts to E on A, along with likewise pertaining to B.

Earthquake theorem

Thurston's earthquake theorem states in which for just about any not one but two details x, y of Kerckhoff (1983) , who employed the item in order to resolve the actual Nielsen recognition difficulty .

References

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

66, Paris:

Low dimensional topology and also Kleinian groups,