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Algebraic and Geometric Surgery

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

The Ambient Metric (AM-178)

The Ambient Metric (AM-178)

Charles Fefferman and C. Robin Graham

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.001.0001
Subject:
Mathematics, Geometry / Topology

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ... More

Arithmetic Compactifications of PEL-Type Shimura Varieties

Arithmetic Compactifications of PEL-Type Shimura Varieties

Kai-Wen Lan

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691156545
eISBN:
9781400846016
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691156545.001.0001
Subject:
Mathematics, Geometry / Topology

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical ... More

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

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

Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.001.0001
Subject:
Mathematics, Geometry / Topology

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ... More

The Decomposition of Global Conformal Invariants (AM-182)

The Decomposition of Global Conformal Invariants (AM-182)

Spyros Alexakis

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.001.0001
Subject:
Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More

Differential GeometryBundles, Connections, Metrics and Curvature

Differential Geometry: Bundles, Connections, Metrics and Curvature

Clifford Henry Taubes

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.001.0001
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

Bundles, connections, metrics, and curvature are the ‘lingua franca’ of modern differential geometry and theoretical physics. Many of the tools used in differential topology are introduced and the ... More

Flips for 3-folds and 4-folds

Flips for 3-folds and 4-folds

Alessio Corti (ed.)

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198570615
eISBN:
9780191717703
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570615.001.0001
Subject:
Mathematics, Geometry / Topology

The minimal model program in algebraic geometry is a conjectural sequence of algebraic surgery operations that simplifies any algebraic variety to a point where it can be decomposed into pieces with ... More

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Isroil A. Ikromov and Detlef Müller

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.001.0001
Subject:
Mathematics, Geometry / Topology

This is the first book to present a complete characterization of Stein–Tomas-type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all ... More

Fourier-Mukai Transforms in Algebraic Geometry

Fourier-Mukai Transforms in Algebraic Geometry

D. Huybrechts

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.001.0001
Subject:
Mathematics, Geometry / Topology

This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this ... More

Geometry and Physics: Volume IA Festschrift in honour of Nigel Hitchin

Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin

Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198802013
eISBN:
9780191840500
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802013.001.0001
Subject:
Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More

Geometry and Physics: Volume IIA Festschrift in honour of Nigel Hitchin

Geometry and Physics: Volume II: A Festschrift in honour of Nigel Hitchin

Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198802020
eISBN:
9780191869068
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802020.001.0001
Subject:
Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More

Hodge Theory (MN-49)

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

Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Jean-Michel Bismut

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691151298
eISBN:
9781400840571
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151298.001.0001
Subject:
Mathematics, Geometry / Topology

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators ... More

Introduction to Symplectic Topology

Introduction to Symplectic Topology

Dusa McDuff and Dietmar Salamon

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198794899
eISBN:
9780191836411
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198794899.001.0001
Subject:
Mathematics, Analysis, Geometry / Topology

Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important ... More

Lectures on Geometry

Lectures on Geometry

Edward Witten, Martin Bridson, Helmut Hofer, Marc Lackenby, and Rahul Pandharipande

N M J Woodhouse (ed.)

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198784913
eISBN:
9780191827150
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198784913.001.0001
Subject:
Mathematics, Geometry / Topology

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. Although not explicitly linked, ... More

4-Manifolds

4-Manifolds

Selman Akbulut

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198784869
eISBN:
9780191827136
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198784869.001.0001
Subject:
Mathematics, Geometry / Topology

This book present the topology of smooth 4-manifolds in an intuitive self-contained way. The handlebody theory, and the seiberg-witten theory of 4-manifolds are presented. Also stein and symplectic ... More

The Many Facets of GeometryA Tribute to Nigel Hitchin

The Many Facets of Geometry: A Tribute to Nigel Hitchin

Oscar Garcia-Prada, Jean Pierre Bourguignon, and Simon Salamon (eds)

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.001.0001
Subject:
Mathematics, Geometry / Topology

Few people have proved more influential in the field of differential and algebraic geometry, and in showing how this links with mathematical physics, than Nigel Hitchin. Oxford University's Savilian ... More

New Perspectives in Stochastic Geometry

New Perspectives in Stochastic Geometry

Wilfrid S. Kendall and Ilya Molchanov (eds)

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.001.0001
Subject:
Mathematics, Geometry / Topology

Stochastic geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, ... More

Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Ehud Hrushovski and François Loeser

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691161686
eISBN:
9781400881222
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161686.001.0001
Subject:
Mathematics, Geometry / Topology

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model ... More

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