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Riemann Surfaces, Coverings, and Hypergeometric Functions

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and ... More


Mirror Symmetry of Fourier—Mukai Transformation for Elliptic Calabi—Yau Manifolds

Naichung Conan Leung and Shing‐Tung Yau

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0015
Subject:
Mathematics, Geometry / Topology

Mirror symmetry conjecture says that for any Calabi–Yau (CY) manifold M near the large complex/symplectic structure limit, there is another CY manifold X, called the mirror manifold, such that the ... More


The Ping-Pong Lemma

Johanna Mangahas

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0005
Subject:
Mathematics, Geometry / Topology

This chapter considers an identifying feature of free groups: their ability to play ping-pong. In mathematics, you may encounter a group without immediately knowing which group it is. Fortunately, ... More


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