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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


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