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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

## Thurston's Proof

*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/9780691147949.003.0016
- Subject:
- Mathematics, Geometry / Topology

This chapter describes Thurston's original path of discovery to the Nielsen–Thurston classification theorem. It first provides an example that illustrates much of the general theory, focusing on ... More

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