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The stable parametrized <i>h</i>-cobordism theorem

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

in Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157757
eISBN:
9781400846528
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157757.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter deals with the stable parametrized h-cobordism theorem. It begins with a discussion of the manifold part; here DIFF is written for the category of Csuperscript infinity smooth manifolds, ... More


A Primer on Mapping Class Groups (PMS-49)

Benson Farb and Dan Margalit

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147949
eISBN:
9781400839049
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147949.001.0001
Subject:
Mathematics, Geometry / Topology

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many ... More


Mobility, circulation, and homeomorphism: data becoming risk information

Nathaniel O’Grady

in Security/Mobility: Politics of Movement

Published in print:
2017
Published Online:
September 2017
ISBN:
9781526107459
eISBN:
9781526124258
Item type:
chapter
Publisher:
Manchester University Press
DOI:
10.7228/manchester/9781526107459.003.0005
Subject:
Political Science, Security Studies

This chapter analyses the British Fire and Rescue Services, in particular how data travel through their digital infrastructures until it is finally computed into risk assessments that intend to ... More


Mapping Class Groups

Leah Childers and Dan Margalit

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/9780691158662.003.0017
Subject:
Mathematics, Geometry / Topology

This chapter considers the mapping class group, the group of symmetries of a surface, and some of its basic properties. It first provides an overview of surfaces and the concept of homeomorphism ... More


Symmetric Markovian Semigroups and Dirichlet Forms

Zhen-Qing Chen and Masatoshi Fukushima

in Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691136059
eISBN:
9781400840564
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691136059.003.0001
Subject:
Mathematics, Probability / Statistics

This chapter studies the concepts of Dirichlet form and Dirichlet space by first working with a σ‎-finite measure space (E,B(E),m) without any topological assumption on E and establish the ... More


Curves, Surfaces, and Hyperbolic Geometry

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/9780691147949.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter explains the basics of working with simple closed curves, focusing on the case of the closed surface Sɡ of genus g. When g is greater than or equal to 2, hyperbolic geometry enters as a ... More


Mapping Class Group Basics

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/9780691147949.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter explains the basics of the mapping class group of a surface. It first provides the definition and examples before computing the mapping class group in essentially all of the cases where ... 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


The Dehn-Nielsen-Baer Theorem

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/9780691147949.003.0009
Subject:
Mathematics, Geometry / Topology

This chapter deals with the Dehn–Nielsen–Baer theorem, one of the most beautiful connections between topology and algebra in the mapping class group. It begins by defining the objects in the ... More


Pseudo-Anosov Theory

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/9780691147949.003.0015
Subject:
Mathematics, Geometry / Topology

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping ... More


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