Download A Comprehensive Introduction to Differential Geometry, Vol. by Michael Spivak PDF

By Michael Spivak

Booklet through Michael Spivak, Spivak, Michael

Show description

Read Online or Download A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition PDF

Best differential geometry books

An Introduction to Noncommutative Geometry

Noncommutative geometry, encouraged via quantum physics, describes singular areas through their noncommutative coordinate algebras and metric constructions through Dirac-like operators. Such metric geometries are defined mathematically by means of Connes' idea of spectral triples. those lectures, brought at an EMS summer time institution on noncommutative geometry and its purposes, supply an outline of spectral triples in accordance with examples.

Geometry, Topology and Quantization

This can be a monograph on geometrical and topological good points which come up in numerous quantization techniques. Quantization schemes examine the feasibility of arriving at a quantum approach from a classical one and those contain 3 significant tactics viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti­ zation.

Complex Spaces in Finsler, Lagrange and Hamilton Geometries

From a historic perspective, the speculation we undergo the current learn has its origins within the well-known dissertation of P. Finsler from 1918 ([Fi]). In a the classical proposal additionally traditional category, Finsler geometry has in addition to a few generalizations, which use a similar paintings strategy and that are thought of self-geometries: Lagrange and Hamilton areas.

Introductory Differential Geometry For Physicists

This ebook develops the maths of differential geometry in a much more intelligible to physicists and different scientists attracted to this box. This publication is essentially divided into three degrees; point zero, the closest to instinct and geometrical adventure, is a quick precis of the speculation of curves and surfaces; point 1 repeats, reviews and develops upon the conventional tools of tensor algebra research and point 2 is an creation to the language of contemporary differential geometry.

Extra info for A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition

Example text

As a piece of notation, a positive symplectic divisor is a union of symplectic surfaces D = ai Σi with ai > 0, with the Σi pairwise having only isolated positive transverse intersections, and no triple intersections. 3 If a symplectic divisor satisfies D · Σj ≥ 0 for all j, then it can be symplectically smoothed. Proof (Sketch). Suppose first that all the Σi are complex curves in a K¨ ahler surface. The hypothesis says that the line bundle O(D) has non-negative degree on each component. Then we can find a smooth section γ of O(D) which is holomorphic near each intersection point and near its (transverse) zero set.

Note that a Lefschetz pencil is a family of symplectic surfaces of arbitrarily large volume and complexity (depending on k), so somewhat different techniques are needed to find symplectic surfaces in a prescribed homology class. 1 Symmetric Products Let (X, ωX ) be a symplectic four-manifold with integral [ωX ], and fix a ˆ → S 2 on the blowLefschetz pencil, giving rise to a Lefschetz fibration f : X ˆ with the symplectic form ωC = p∗ ωX + C f ∗ ωS 2 up. We will always equip X for some large C > 0.

Generic hyperplane sections of this projective embedding are smooth hypersurfaces in M , and a pencil of hyperplanes through a generic codimension 2 linear subspace defines a Lefschetz pencil. When the manifold M is only symplectic, the lack of integrability of J prevents the existence of holomorphic sections. Nonetheless, it is possible to find an approximately holomorphic local model: a neighborhood of a point 18 D. Auroux and I. Smith x ∈ M , equipped with the symplectic form ω and the almost-complex structure J, can be identified with a neighborhood of the origin in Cn equipped with the standard symplectic form ω0 and an almost-complex structure of the form i + O(|z|).

Download PDF sample

Rated 4.41 of 5 – based on 47 votes