The Torus Does Not Have a Hyperbolic Structure

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Description

Several basic topics from Algebraic Topology, including fundamental group and universal covering space are shown. The hyperbolic plane is defined, including its metric and show what the "straight" lines are in the plane and what the isometries are on the plane. A hyperbolic surface is defined, and shows that the two hole torus is a hyperbolic surface, the hyperbolic plane is a universal cover for any hyperbolic surface, and the quotient space of the universal cover of a surface to the group of automorphisms on the covering space is equivalent to the original surface.

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iii, 29 leaves : ill.

Creation Information

Butler, Joe R. August 1992.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 15 times . More information about this thesis can be viewed below.

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  • Butler, Joe R.

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Description

Several basic topics from Algebraic Topology, including fundamental group and universal covering space are shown. The hyperbolic plane is defined, including its metric and show what the "straight" lines are in the plane and what the isometries are on the plane. A hyperbolic surface is defined, and shows that the two hole torus is a hyperbolic surface, the hyperbolic plane is a universal cover for any hyperbolic surface, and the quotient space of the universal cover of a surface to the group of automorphisms on the covering space is equivalent to the original surface.

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iii, 29 leaves : ill.

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UNT Theses and Dissertations

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  • August 1992

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  • March 9, 2015, 8:15 a.m.

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  • Sept. 6, 2017, 8:22 a.m.

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Citations, Rights, Re-Use

Butler, Joe R. The Torus Does Not Have a Hyperbolic Structure, thesis, August 1992; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc500333/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .