## INTRODUCTION

*Pavol Hell and Jaroslav Nešetřil*

### in Graphs and Homomorphisms

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This introductory chapter is a sampler of the material covered in the book. It introduces the notation and terminology in the book, and provides motivational examples and applications, many taken up ... More

## THE PARTIAL ORDER OF GRAPHS AND HOMOMORPHISMS

*Pavol Hell and Jaroslav Nešetřil*

### in Graphs and Homomorphisms

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.003.0003
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the order homomorphisms induce on the set of all cores; this order is rich enough to represent all countable partial orders. Antichains in the homomorphism order are discussed, ... More

## THE STRUCTURE OF COMPOSITION

*Pavol Hell and Jaroslav Nešetřil*

### in Graphs and Homomorphisms

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.003.0004
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on the structure, as opposed to just the existence, of the family of homomorphisms among a set of graphs. The difference is noticeable with even just one graph. For instance, a ... More

## TESTING FOR THE EXISTENCE OF HOMOMORPHISMS

*Pavol Hell and Jaroslav Nešetřil*

### in Graphs and Homomorphisms

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.003.0005
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter explores the algorithmic aspects of graph homomorphisms and of similar partition problems. The highlights include the dichotomy classification of graph homomorphisms to a fixed target ... More

## Completely isomorphic theory of operator algebras

*David P. Blecher and Christian Le Merdy*

### in Operator Algebras and Their Modules: An operator space approach

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198526599
- eISBN:
- 9780191712159
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526599.003.0005
- Subject:
- Mathematics, Pure Mathematics

This chapter studies operator algebras ‘up to isomorphism’ or ‘up to complete isomorphism’. Topics covered include homomorphisms of operator algebras, completely bounded characterizations, examples ... More

## BUNDLES

*Andrew Ranicki*

### in Algebraic and Geometric Surgery

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198509240
- eISBN:
- 9780191708725
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509240.003.0005
- Subject:
- Mathematics, Geometry / Topology

This chapter brings together the basic properties of fibre bundles, fibrations, and vector bundles required in surgery theory. The tangent and normal bundles of a manifold are introduced. The ... More

## Mumford-Tate Groups

*Mark Green, Phillip Griffiths, and Matt Kerr*

### in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691154244
- eISBN:
- 9781400842735
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691154244.003.0002
- Subject:
- Mathematics, Analysis

This chapter provides an introduction to the basic definitions and properties of Mumford-Tate groups in both the case of Hodge structures and of mixed Hodge structures. Hodge structures of weight n ... More

## Foundations of a Measurement‐Theoretic Account of the Attitudes

*Robert J. Matthews*

### in The Measure of Mind: Propositional Attitudes and their Attribution

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199211258
- eISBN:
- 9780191705724
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211258.003.0005
- Subject:
- Philosophy, Philosophy of Mind

This chapter begins with a brief introduction to the numerical measurement theory upon which the ‘measurement-theoretic’ account of the attitudes will be modeled. Topics covered include the ... More

## Resultatives Under the ‘Event-Argument Homomorphism’ Model of Telicity

*STEPHEN WECHSLER*

### in The Syntax of Aspect: Deriving Thematic and Aspectual Interpretation

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780199280445
- eISBN:
- 9780191712845
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199280445.003.0012
- Subject:
- Linguistics, Syntax and Morphology

This chapter presents a novel semantic analysis of the English resultative construction that crucially models telicity (aspectual boundedness) in terms of the event-argument homomorphism model ... More

## Dehn Twists

*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/9780691147949.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with Dehn twists, the simplest infinite-order elements of Mod(S). It first defines Dehn twists and proves that they are nontrivial elements of the mapping class group. In ... More

## 2 2 Lexical aspect and multiple incremental themes

*John Beavers*

### in Telicity, Change, and State: A Cross-Categorial View of Event Structure

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199693498
- eISBN:
- 9780191741715
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199693498.003.0002
- Subject:
- Linguistics, Semantics and Pragmatics, Syntax and Morphology

Aspectual properties of dynamic predicates such as telicity and durativity are often assumed to be partly determined by the expression of some privileged argument of the predicate called an ... More

## The group of symplectomorphisms

*Dusa McDuff and Dietmar Salamon*

### in Introduction to Symplectic Topology

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198794899
- eISBN:
- 9780191836411
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198794899.003.0011
- Subject:
- Mathematics, Analysis, Geometry / Topology

This chapter discusses the basic properties of the group of symplectomorphisms of a compact connected symplectic manifold and its subgroup of Hamiltonian symplectomorphisms. It begins by showing that ... More

## General Properties of Equivariant Cohomology

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0009
- Subject:
- Mathematics, Educational Mathematics

This chapter assesses the general properties of equivariant cohomology. Both the homotopy quotient and equivariant cohomology are functorial constructions. Equivariant cohomology is particularly ... More

## A Crash Course in Representation Theory

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0027
- Subject:
- Mathematics, Educational Mathematics

This chapter studies representation theory. In order to state the equivariant localization formula of Atiyah–Bott and Berline–Vergne, one will need to know some representation theory. Representation ... More

## Introduction to vector bundles

*Clifford Henry Taubes*

### in Differential Geometry: Bundles, Connections, Metrics and Curvature

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199605880
- eISBN:
- 9780191774911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199605880.003.0003
- Subject:
- Mathematics, Geometry / Topology, Mathematical Physics

This chapter examines vector bundles. It begins with a standard definition of vector bundles, and this is followed by some first examples of vector bundles. It then discusses the tangent bundle with ... More

## Algebra of vector bundles

*Clifford Henry Taubes*

### in Differential Geometry: Bundles, Connections, Metrics and Curvature

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199605880
- eISBN:
- 9780191774911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199605880.003.0004
- Subject:
- Mathematics, Geometry / Topology, Mathematical Physics

Any linear operation that can be performed to generate a new vector space from a given set of initial vector spaces can be done fibre-wise with an analogous set of vector bundles to generate a new ... More

## Causally Driven Analogs

*Karen Neander*

### in A Mark of the Mental: In Defense of Informational Teleosemantics

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780262036146
- eISBN:
- 9780262339865
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262036146.003.0008
- Subject:
- Philosophy, Philosophy of Mind

In chapter 8, the author brings causal, teleosemantic and resemblance theories of content together by extending CT (as presented in chapter 7) to explain how homomorphism (more specifically, analog ... More

## Groups

*Matt Clay 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/9780691158662.003.0001
- Subject:
- Mathematics, Geometry / Topology

This chapter considers the notion of a group in mathematics. It begins with a discussion of the problem of determining the symmetry of an object such as a planar shape, a higher-dimensional solid, a ... More

## Preliminary notions

*Brian Conrad and Gopal Prasad*

### in Classification of Pseudo-reductive Groups (AM-191)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691167923
- eISBN:
- 9781400874026
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167923.003.0002
- Subject:
- Mathematics, Numerical Analysis

This chapter considers some preliminary notions, starting with standard pseudo-reductive groups, Levi subgroups, and root systems. It reviews the “standard construction” of pseudo-reductive k-groups ... More

## An Account of Similarity

*Michael Weisberg*

### in Simulation and Similarity: Using Models to Understand the World

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199933662
- eISBN:
- 9780199333004
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199933662.003.0008
- Subject:
- Philosophy, Philosophy of Science

This chapter develops the weighted feature-matching account of similarity. Most accounts of the model–world relation draw on logical properties such as isomorphism and homomorphism. In contrast, ... More