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Geometric transitions : from hyperbolic to Ads geometry

저자: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
출판사: 2011.
논문: Thesis (Ph. D.)--Stanford University, 2011.
판/형식:   주제/주장 : 문서 : 눈문/학위논문 : 전자도서   컴퓨터 파일 : 영어
데이터베이스:WorldCat
요약:
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds  더 읽기…
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자료 유형: 문서, 눈문/학위논문, 인터넷 자료
문서 형식: 인터넷 자원, 컴퓨터 파일
모든 저자 / 참여자: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
OCLC 번호: 743406573
메모: Submitted to the Department of Mathematics.
설명: 1 online resource.
책임: Jeffrey Danciger.

초록:

We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds generated on the "other side" of the transition have tachyon singularities. The method involves the study of a new transitional geometry called half-pipe geometry. We also discuss combinatorial/algebraic tools for constructing transitions using ideal tetrahedra. Using these tools we prove that transitions can always be constructed when the underlying manifold is a punctured torus bundle.

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