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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


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