## Algebraic and Geometric Surgery

*Andrew Ranicki*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509240.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book is an introduction to surgery theory, the standard algebraic topology classification method for manifolds of dimension greater than 4. It is aimed at those who have already been on a basic ... More

## General Relativity and the Einstein Equations

*Yvonne Choquet-Bruhat*

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.001.0001
- Subject:
- Mathematics, Applied Mathematics

General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these ... More

## Synergy

*Mark L. Latash*

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780195333169
- eISBN:
- 9780199864195
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195333169.001.0001
- Subject:
- Neuroscience, Sensory and Motor Systems, Techniques

This book discusses a general problem in biology: the lack of an adequate language for formulating biologically specific problems. This book describes recent progress in the control and coordination ... More

## Chern-Simons Theory, Matrix Models, and Topological Strings

*Marcos Mariño*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568490
- eISBN:
- 9780191717604
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568490.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string ... More

## STRING THEORY AND GAUGE THEORY

*Marcos Mariño*

### in Chern-Simons Theory, Matrix Models, and Topological Strings

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568490
- eISBN:
- 9780191717604
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568490.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines the relationship between gauge theories and topological strings. A precise correspondence between string theory and gauge theory was formulated by 't Hooft (1974), who used as a ... More

## Sasakian Geometry in Dimensions 3 and 5

*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/9780198564959.003.0011
- Subject:
- Mathematics, Geometry / Topology

This chapter describes Sasakian geometry in low dimensions. In dimension three there is a complete classification; dimension five is large enough to be interesting, yet small enough to hope for some ... More

## The manifold part

*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/9780691157757.003.0005
- Subject:
- Mathematics, Geometry / Topology

This chapter reduces the proof of the manifold part of the stable parametrized h-cobordism theorem to a result about spaces of stably framed manifolds. Here Δsuperscript q denotes the standard ... 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

## Symmetries 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/9780198564959.003.0009
- Subject:
- Mathematics, Geometry / Topology

This chapter presents known results concerning symmetries of Sasakian structures, including a detailed study of the Sasakian automorphisms and various deformations of Sasakian structures. Homogeneous ... More

## Sasakian Structures, Killing Spinors, and Supersymmetry

*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/9780198564959.003.0015
- Subject:
- Mathematics, Geometry / Topology

This chapter gives a very brief overview of the rich theory of Killing spinors describing Bär's correspondence which connects Sasaki-Einstein geometry to Berger's holonomy theorem. It is then shown ... More

## THE NEUMANN PROBLEM AND PROBLEMS ON MANIFOLDS

*Juan Luis Vázquez*

### in The Porous Medium Equation: Mathematical Theory

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198569039
- eISBN:
- 9780191717468
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198569039.003.0011
- Subject:
- Mathematics, Mathematical Physics

This chapter completes the investigation of previous chapters on the Dirichlet and Cauchy problems by applying the techniques to other important problems. It selects two directions, the Neumann ... More

## Twistor methods

*Paul Baird and John C. Wood*

### in Harmonic Morphisms Between Riemannian Manifolds

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0007
- Subject:
- Mathematics, Pure Mathematics

This chapter discusses how twistor methods can be used to construct nonconstant harmonic morphisms from (orientable) Einstein 4-manifolds to Riemann surfaces. It is shown that any such map induces an ... More

## Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

*Friedhelm Waldhausen, Bjørn Jahren, and John Rognes*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691157757
- eISBN:
- 9781400846528
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691157757.001.0001
- Subject:
- Mathematics, Geometry / Topology

Since its introduction by the author in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a ... More

## Branes on Poisson Varieties

*Marco Gualtieri*

### 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/9780199534920.003.0018
- Subject:
- Mathematics, Geometry / Topology

This chapter takes a second look at a classical structure in differential and algebraic geometry — that of a holomorphic Poisson structure — which is a complex manifold with a holomorphic Poisson ... More

## Introduction

*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/9780691157757.003.0001
- Subject:
- Mathematics, Geometry / Topology

This book presents a proof of the stable parametrized h-cobordism theorem, which deals with the existence of a natural homotopy equivalence for each compact CAT manifold. In this theorem, a stable ... More

## Kähler Manifolds

*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/9780198564959.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter reviews some basic facts about Kähler manifolds with special emphasis on projective algebraic varieties. All standard material is covered: complex structures, curvature properties, Hodge ... More

## Quaternionic Kähler and Hyperkähler Manifolds

*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/9780198564959.003.0013
- Subject:
- Mathematics, Geometry / Topology

This chapter gives an extensive overview of various quaternionic geometries. The main focus is on positive quaternionic Kähler manifolds (orbifolds) and on hyper Kähler manifolds (orbifolds). Various ... More

## 3-Sasakian Manifolds

*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/9780198564959.003.0014
- Subject:
- Mathematics, Geometry / Topology

This chapter introduces a special case of Sasaki-Einstein manifolds which have a somewhat richer structure and occur only in dimensions 4m + 3. As any Sasakian manifold they are foliated by ... More

## Observer-independent Dynamical Measures of Team Coordination and Performance

*Silke M. Dodel, Ajay S. Pillai, Philip W. Fink, Eric R. Muth, Roy Stripling, Dylan D. Schmorrow, Joseph V. Cohn, and Viktor K. Jirsa*

### in Motor Control: Theories, Experiments, and Applications

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780195395273
- eISBN:
- 9780199863518
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195395273.003.0004
- Subject:
- Neuroscience, Sensory and Motor Systems

Team performance represents an extension of individual performance. It is an outcome of individuals joining together for the purpose of exploiting one another's individual skills to accomplish ... More

## Mini-twistor theory on three-dimensional space forms

*Paul Baird and John C. Wood*

### in Harmonic Morphisms Between Riemannian Manifolds

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0006
- Subject:
- Mathematics, Pure Mathematics

This chapter discusses harmonic morphisms from 3-manifolds to surfaces, especially those of constant curvature. First, the local behaviour is considered, showing that the foliation given by its ... More