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Geometry with an Introduction to Cosmic Topology
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  • Title: Geometry with an Introduction to Cosmic Topology
  • Author(s) Michael P. Hitchman
  • Publisher: CreateSpace (June 8, 2018); eBook (2020 Edition, Creative Commons Licensed)
  • License(s): CC BY 4.0
  • Paperback: 275 pages
  • eBook: HTML and PDF
  • Language: English
  • ASIN/ISBN-10: 1717134815
  • ISBN-13: 978-1717134813
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Book Description

This book follows the Erlangen program to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.

The text uses Mobius transformations in the extended complex plane to define and investigate these three candidate geometries, thereby providing a natural setting in which to express results common to them all, as well as results that encapsulate key differences.

With these geometries in hand, the text then explores the interplay between the shape of a space and the type of geometry it admits.

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