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Dynamics on the Moduli Space of Non-Orientable Surfaces.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Dynamics on the Moduli Space of Non-Orientable Surfaces./
Author:	Khan, Sayantan.
Description:	1 online resource (126 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798382739304

Dynamics on the Moduli Space of Non-Orientable Surfaces.
Khan, Sayantan.

Dynamics on the Moduli Space of Non-Orientable Surfaces. - 1 online resource (126 pages)

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Thesis (Ph.D.)--University of Michigan, 2024.

Includes bibliographical references

The moduli spaces of non-orientable hyperbolic surfaces have conjectural similarities to infinite volume geometrically finite hyperbolic manifolds. This thesis establishes some of the conjectured analogies to geometrically finite hyperbolic manifolds, which are useful in the context of understanding the geodesic flow on the unit cotangent bundle of the moduli space. In particular, it is shown that the Patterson-Sullivan measure is supported on the set of projective measured foliations containing no one-sided leaves. We then also show that the action of the mapping class group on the Teichmuller space, restricted to a finite covolume subset, is statistically convex-cocompact. We deduce from this that the Patterson-Sullivan measure is non-atomic, and the Bowen-Margulis measure on the unit cotangent bundle is finite, and the geodesic flow is ergodic with respect to this measure.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798382739304Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

GeometryIndex Terms--Genre/Form:

554714
Electronic books.

Dynamics on the Moduli Space of Non-Orientable Surfaces.
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500 $a Advisor: Wright, Alexander;Spatzier, Ralf.
502 $a Thesis (Ph.D.)--University of Michigan, 2024.
504 $a Includes bibliographical references
520 $a The moduli spaces of non-orientable hyperbolic surfaces have conjectural similarities to infinite volume geometrically finite hyperbolic manifolds. This thesis establishes some of the conjectured analogies to geometrically finite hyperbolic manifolds, which are useful in the context of understanding the geodesic flow on the unit cotangent bundle of the moduli space. In particular, it is shown that the Patterson-Sullivan measure is supported on the set of projective measured foliations containing no one-sided leaves. We then also show that the action of the mapping class group on the Teichmuller space, restricted to a finite covolume subset, is statistically convex-cocompact. We deduce from this that the Patterson-Sullivan measure is non-atomic, and the Bowen-Margulis measure on the unit cotangent bundle is finite, and the geodesic flow is ergodic with respect to this measure.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
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650 4 $a Theoretical mathematics. $3 1180455
653 $a Geometry
653 $a Topology
653 $a Dynamics
653 $a Finite hyperbolic manifold
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