Oxford Index Browse

You are looking at 1-10 of 174 items for:

Geometry x clear all

Refine by type

Refine by product

 

ABELIAN VARIETIES

D. Huybrechts.

in Fourier-Mukai Transforms in Algebraic Geometry

April 2006; p ublished online September 2007 .

Chapter. Subjects: Geometry. 18844 words.

Historically, Mukai's equivalence with the Poincare bundle on the product of an abelian variety and its dual as kernel was the fist Fourier-Mukai transform. The first section in this...

Go to Oxford Scholarship Online »  abstract

Algebra of vector bundles

Clifford Henry Taubes.

in Differential Geometry

October 2011; p ublished online December 2013 .

Chapter. Subjects: Geometry. 4008 words.

Any linear operation that can be performed to generate a new vector space from a given set of initial vector spaces can be done fibre-wise with an analogous set of vector bundles to...

Go to Oxford Scholarship Online »  abstract

Algebraic and Geometric Surgery

Andrew Ranicki.

September 2002; p ublished online September 2007 .

Book. Subjects: Geometry. 386 pages.

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...

Go to Oxford Scholarship Online »  abstract

Almost complex structures

Dusa McDuff and Dietmar Salamon.

in Introduction to Symplectic Topology

March 2017; p ublished online June 2017 .

Chapter. Subjects: Mathematics; Geometry. 20797 words.

The chapter begins with a general discussion of almost complex structures on symplectic manifolds and then addresses the problem of integrability. Subsequent sections discuss a variety of...

Go to Oxford Scholarship Online »  abstract

Almost Contact and Contact Geometry

Charles P. Boyer and Krzysztof Galicki.

in Sasakian Geometry

October 2007; p ublished online January 2008 .

Chapter. Subjects: Geometry. 17159 words.

This chapter presents the necessary foundational material on almost contact, contact, and metric contact structures. The key result is an orbifold version of the famous Boothby-Wang...

Go to Oxford Scholarship Online »  abstract

Applications of Stochastic Geometry in Image Analysis

Marie‐Colette N.M. van Lieshout.

in New Perspectives in Stochastic Geometry

November 2009; p ublished online February 2010 .

Chapter. Subjects: Geometry. 11152 words.

A discussion is given of various stochastic geometry models (random fields, sequential object processes, polygonal field models) which can be used in intermediate‐ and high‐level image...

Go to Oxford Scholarship Online »  abstract

Applications of the Euler characteristic

Simon Donaldson.

in Riemann Surfaces

March 2011; p ublished online December 2013 .

Chapter. Subjects: Geometry. 4464 words.

The genus of a compact oriented smooth surface S can be defined as one-half the dimension of the de Rham cohomology group H 1(S). Another way of defining the genus involves the...

Go to Oxford Scholarship Online »  abstract

Area-preserving diffeomorphisms

Dusa McDuff and Dietmar Salamon.

in Introduction to Symplectic Topology

March 2017; p ublished online June 2017 .

Chapter. Subjects: Mathematics; Geometry. 6582 words.

This chapter is devoted to two-dimensional symplectomorphisms, which are just area- and orientation-preserving diffeomorphisms. The chapter includes an exposition of Birkhoff’s proof of...

Go to Oxford Scholarship Online »  abstract

The arnold conjecture

Dusa McDuff and Dietmar Salamon.

in Introduction to Symplectic Topology

March 2017; p ublished online June 2017 .

Chapter. Subjects: Mathematics; Geometry. 21002 words.

This chapter contains a proof of the Arnold conjecture for the standard torus, which is based on the discrete symplectic action. The symplectic part of this proof is very easy. However, for...

Go to Oxford Scholarship Online »  abstract

Basic definitions

Simon Donaldson.

in Riemann Surfaces

March 2011; p ublished online December 2013 .

Chapter. Subjects: Geometry. 6116 words.

This chapter presents definitions of Riemann surfaces and holomorphic maps, and provides examples, including algebraic curves and quotients.

Go to Oxford Scholarship Online »  abstract