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Dynamics on the Moduli Space of Non-...

Khan, Sayantan.

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Dynamics on the Moduli Space of Non-Orientable Surfaces.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Dynamics on the Moduli Space of Non-Orientable Surfaces./
作者:	Khan, Sayantan.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2024,
面頁冊數:	126 p.
附註:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31348953
ISBN:	9798382739304

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

Dynamics on the Moduli Space of Non-Orientable Surfaces. - Ann Arbor : ProQuest Dissertations & Theses, 2024 - 126 p.

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

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

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.

ISBN: 9798382739304Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Geometry

Dynamics on the Moduli Space of Non-Orientable Surfaces.
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300 $a 126 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
500 $a Advisor: Wright, Alexander;Spatzier, Ralf.
502 $a Thesis (Ph.D.)--University of Michigan, 2024.
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.
590 $a School code: 0127.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Geometry
653 $a Topology
653 $a Dynamics
653 $a Finite hyperbolic manifold
690 $a 0405
690 $a 0642
710 2 $a University of Michigan. $b Mathematics. $3 3185260
773 0 $t Dissertations Abstracts International $g 85-12B.
790 $a 0127
791 $a Ph.D.
792 $a 2024
793 $a English
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