## 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

## 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

## 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.

## Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

*Claire Voisin*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691160504
- eISBN:
- 9781400850532
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160504.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. ... More

## Hodge Theory (MN-49)

*Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dung Tráng*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161341
- eISBN:
- 9781400851478
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161341.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The ... More

## Differential geometry, topology and fibre bundles

*Reinhold A. Bertlmann*

### in Anomalies in Quantum Field Theory

- Published in print:
- 2000
- Published Online:
- February 2010
- ISBN:
- 9780198507628
- eISBN:
- 9780191706400
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507628.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces all necessary mathematical concepts. Section 2.1 briefly summarizes some topological definitions. Section 2.2 explains the homotopy of maps and the homotopy of groups. Section ... More

## Local Shimura Varieties: Minicourse Given by Peter Scholze

*Gisbert Wüstholz and Clemens Fuchs (eds)*

### in Arithmetic and Geometry: Ten Years in Alpbach

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691193779
- eISBN:
- 9780691197548
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691193779.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses Peter Scholze's minicourse on local Shimura varieties. The goal of these lectures is to describe a program to construct local Langlands correspondence. The construction is ... More

## The Hodge Theory of Maps

*Mark Andrea de Cataldo, Luca Migliorini Lectures 4–5, and Mark Andrea de Cataldo*

*Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)*

### in Hodge Theory (MN-49)

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161341
- eISBN:
- 9781400851478
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161341.003.0006
- Subject:
- Mathematics, Geometry / Topology

This chapter showcases two further lectures on the Hodge theory of maps, and they are mostly composed of exercises. The first lecture details a minimalist approach to sheaf cohomology, and then turns ... More

## An Invitation to Computational Homotopy

*Graham Ellis*

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198832973
- eISBN:
- 9780191871375
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198832973.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization, Geometry / Topology

This book is an introduction to elementary algebraic topology for students with an interest in computers and computer programming. Its aim is to illustrate how the basics of the subject can be ... More

## Hilbert 90 for KnM

*Christian Haesemeyer and Charles A. Weibel*

### in The Norm Residue Theorem in Motivic Cohomology

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691191041
- eISBN:
- 9780691189635
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191041.003.0003
- Subject:
- Mathematics, Geometry / Topology

This chapter formulates a norm-trace relation for the Milnor 𝐾-theory and étale cohomology of a cyclic Galois extension, herein called Hilbert 90 for 𝐾𝑀𝑛. To begin, the chapter uses condition BL(n) ... More