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Fundamentals of Orbifolds

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0005
Subject:
Mathematics, Geometry / Topology

A key tool that allows for connecting Sasakian structures to other geometric structures is the theory of Kähler orbifolds and their orbifold bundles or ‘orbibundles’. Orbifolds, just as manifolds, ... More


Kähler–Einstein Metrics

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter is a second trip into the realm of Kähler geometry, focusing on Kähler-Einstein metrics, in particular positive scalar curvature Kähler-Einstein metrics on compact Fano orbifolds, which ... More


Harmonic morphisms from compact 3-manifolds

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0010
Subject:
Mathematics, Pure Mathematics

This chapter shows that a non-constant harmonic morphism with compact fibres from a 3-manifold endows it with the structure of a Seifert fibre space — a 3-manifold with a certain type of ... More


Existence of Ball Quotients Covering Line Arrangements

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/9780691144771.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter justifies the assumption that ball quotients covering line arrangements exist. It begins with the general case on the existence of finite covers by ball quotients of weighted ... More


Introduction

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/9780691144771.003.0001
Subject:
Mathematics, Geometry / Topology

This chapter explains that the book deals with quotients of the complex 2-ball yielding finite coverings of the projective plane branched along certain line arrangements. It gives a complete list of ... More


Torsion

Benson Farb and Dan Margalit

in A Primer on Mapping Class Groups (PMS-49)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147949
eISBN:
9781400839049
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147949.003.0008
Subject:
Mathematics, Geometry / Topology

This chapter deals with finite subgroups of the mapping class group. It first explains the distinction between finite-order mapping classes and finite-order homeomorphisms, focusing on the Nielsen ... More


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