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The Fourth Janko Group

Alexander A. Ivanov

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198527596
eISBN:
9780191713163
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527596.001.0001
Subject:
Mathematics, Pure Mathematics

This book illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory, and local analysis, are combined to construct one of ... More


Derived Category and Canonical Bundle --II

D. Huybrechts

in Fourier-Mukai Transforms in Algebraic Geometry

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.003.0006
Subject:
Mathematics, Geometry / Topology

Based on the work of Orlov, Kawamata, and others, this chapter shows that the (numerical) Kodaira dimension and the canonical ring are preserved under derived equivalence. The same techniques can be ... More


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

Mark Green, Phillip A. Griffiths, and Matt Kerr

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.001.0001
Subject:
Mathematics, Analysis

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive ... More


Foliations

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/9780198564959.003.0003
Subject:
Mathematics, Geometry / Topology

As Sasakian manifolds are all examples of Riemannian foliations with one-dimensional leaves, this chapter goes into the world of foliations with a particular focus on the Riemannian case. Haeiger ... More


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


K-Contact and Sasakian Structures

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/9780198564959.003.0008
Subject:
Mathematics, Geometry / Topology

This chapter begins the study of Sasakian geometry, where all important structure theorems are presented. It then gathers all the results concerning the geometry, topology, and curvature properties ... More


PENTAD GROUP 23+12 · (L 3(2) × Sym5)

A. A. Ivanov

in The Fourth Janko Group

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198527596
eISBN:
9780191713163
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527596.003.0004
Subject:
Mathematics, Pure Mathematics

This chapter discusses the geometric subgroup at level 2 of the modified amalgam G, known as the pentad group, which has a rather complicated structure. The structure can be described in terms of the ... More


COHOMOLOGICAL METHODS IN INFINITE SOLUBLE GROUP THEORY

John C. Lennox and Derek J. S. Robinson

in The Theory of Infinite Soluble Groups

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198507284
eISBN:
9780191709326
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507284.003.0010
Subject:
Mathematics, Pure Mathematics

This chapter talks about cohomological methods in soluble group theory, soluble groups with finite (co)homological dimension, vanishing theorems, applications to near splitting and conjugacy, and ... More


HOMOTOPY AND HOMOLOGY

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/9780198509240.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter serves as a recollection of basic algebraic topology, including mention of homology and cohomology, and homotopy groups. It details intersections and cup product pairing. Attaching cells ... More


An Introduction to Bundle Gerbes

Michael K. Murray

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0012
Subject:
Mathematics, Geometry / Topology

This chapter focuses on bundle gerbes, which provide a geometric realisation of the three dimensional cohomology of a manifold. It shows that the pattern of a p-gerbe being defined as a (p - 1)-gerbe ... More


The Norm Residue Theorem in Motivic Cohomology

Christian Haesemeyer and Charles A. Weibel

Published in print:
2019
Published Online:
January 2020
ISBN:
9780691191041
eISBN:
9780691189635
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691191041.001.0001
Subject:
Mathematics, Geometry / Topology

This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these ... More


Overview

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/9780691191751.003.0001
Subject:
Mathematics, Educational Mathematics

This chapter provides an overview of equivariant cohomology. Cohomology in any of its various forms is one of the most important inventions of the twentieth century. A functor from topological spaces ... More


Double Resonance: Forcing Equivalence

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter assesses the choice of cohomology and Aubry-Mather type at the double resonance. It begins by choosing cohomology classes for the (unperturbed) slow mechanical system. As in the case of ... More


Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions: (AMS-203)

Anantharam Raghuram and Günter Harder

Published in print:
2019
Published Online:
September 2020
ISBN:
9780691197890
eISBN:
9780691197937
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691197890.001.0001
Subject:
Mathematics, Number Theory

This book studies the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of ... More


Borel Localization for a Circle Action

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/9780691191751.003.0026
Subject:
Mathematics, Educational Mathematics

This chapter explores Borel localization for a circle action. For a circle action, the Borel localization theorem says that up to torsion, the equivariant cohomology of an S1-manifold is concentrated ... More


Weil's Conjecture for Function Fields: Volume I (AMS-199)

Dennis Gaitsgory and Jacob Lurie

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691182148
eISBN:
9780691184432
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691182148.001.0001
Subject:
Mathematics, Mathematical Finance

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at ... More


Introductory Lectures on Equivariant Cohomology: (AMS-204)

Loring W. Tu

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691191751
eISBN:
9780691197487
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691191751.001.0001
Subject:
Mathematics, Educational Mathematics

Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into ... More


The Hodge star

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/9780199605880.003.0019
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This chapter first provides a definition of the Hodge star. It then discusses representatives of De Rham cohomology; presents the Hodge theorem; and explains the notion of self-duality.


Spectral Sequences

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/9780691191751.003.0006
Subject:
Mathematics, Educational Mathematics

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined ... More


Equivariant Cohomology of S2 Under Rotation

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/9780691191751.003.0007
Subject:
Mathematics, Educational Mathematics

This chapter shows how to use the spectral sequence of a fiber bundle to compute equivariant cohomology. As an example, it computes the equivariant cohomology of S2 under the action of S1 by ... More


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