Introduction a la Topologie by Nier F., Iftimie D.

By Nier F., Iftimie D.

Ce cours de topologie a été dispensé en licence à l'Université de Rennes 1 de 1999 à 2002. Toutes les constructions permettant de parler de limite et de continuité sont d'abord dégagées, puis l'utilité de l. a. compacité pour ramener des problèmes de complexité infinie à l'étude d'un nombre fini de cas est explicitée. Les premiers rudiments d'analyse fonctionnelle sont ensuite introduits : prédiction de l'existence de los angeles limite d'une suite dans un espace bien défini ; contrôle uniforme d'une régularité... Ce cours se termine sur los angeles généralisation à l. a. size infinie de l. a. concept d'espace euclidien. Il comprend de nombreux exemples et environ one hundred fifty exercices non corrigés.

Show description

Actes de la Table ronde de geometrie differentielle: En by Arthur L. Besse (Ed.)

By Arthur L. Besse (Ed.)

Résumé :
En juillet 1992, une desk Ronde de Géométrie Différentielle s'est tenue au CIRM de Luminy en l'honneur de Marcel Berger. Les conférences qui sont reproduites dans ces Actes recouvrent l. a. plupart des sujets abordés par Marcel Berger en Géométrie Différentielle et plus précisément : l'holonomie (Bryant), los angeles courbure [courbure sectionnelle confident (Grove), courbure sectionnelle négative (Abresch et Schroeder, Ballmann et Ledrappier), courbure de Ricci négative (Lohkamp), courbure scalaire (Delanoë, Hebey et Vaugon), courbure totale (Shioya)], le spectre du laplacien (Anné, Colin de Verdière, Matheus, Pesce), les inégalités isopérimétriques et les systoles (Calabi, Carron, Gromov), ainsi que quelques sujets annexes [espaces d'Alexandrov (Shiohama et Tanaka, Yamaguchi), elastica (Koiso), géométrie sous-riemannienne (Valère et Pelletier)]. Les auteurs sont pour los angeles plupart des géomètres confirmés, dont plusieurs ont travaillé avec Marcel Berger, mais aussi quelques jeunes. Plusieurs articles (Bryant, Colin, Grove...) contiennent une présentation synthétique des résultats récents dans le domaine concerné, pour mieux les rendre obtainable à un public de non-spécialistes.

Abstract:
Proceedings of the around desk in Differential Geometry in honour of Marcel Berger
July 1992, a around desk in Differential Geometry used to be geared up on the CIRM in Luminy (France) in honour of Marcel Berger. In those complaints, contributions disguise lots of the fields studied via Marcel Berger in Differential Geometry, particularly : holonomy (Bryant), curvature [positive sectional curvature (Grove), destructive sectional curvature (Abresch and Schroeder, Ballmann and Ledrappier), adverse Ricci curvature (Lohkamp), scalar curvature (Delanoë, Hebey and Vaugon), overall curvature (Shioya)], spectrum of the Laplacian (Anné, Colin de Verdière, Matheus, Pesce), isoperimetric and isosystolic inequalities (Calabi, Carron, Gromov), including a few similar topics [Alexandrov areas (Shiohama and Tanaka, Yamaguchi), elastica (Koiso), subriemannian geometry (Valère and Pelletier)]. Authors are usually geometers who labored with Marcel Berger at a while, and in addition a few more youthful ones. a few papers (Bryant, Colin, Grove...) contain a short evaluate of modern ends up in their specific fields, with the non-experts in brain.

1. time table of the Mathematical talks given on the around Table

Lundi thirteen juillet 1992

K. GROVE : challenging and smooth sphere theorems
T. YAMAGUCHI : A convergence theorem for Alexandrov spaces
J. LOKHAMP : Curvature h-principles
G. ROBERT : Pinching theorems less than quintessential speculation for curvature

Mardi 14 juillet 1992

Y. COLIN DE VERDIERE : Spectre et topologie
H. PESCE : Isospectral nilmanifolds
F. MATHEUS : Circle packings and conformal approximation
R. MICHEL : From warmth equation to Hamilton-Jacobi equation
C. ANNE : Formes diff´erentielles sur les vari´et´es avec des anses fines
G. CARRON : In´egalit´e isop´erim´etrique de Faber-Krahn

Mercredi 15 juillet 1992

E. CALABI : in the direction of extremal metrics for isosystolic inequality for closed orientable
surfaces with genus > 1
M. GROMOV : Isosystols
Ch. CROKE : Which Riemannian manifolds are decided via their geodesic flows

Jeudi sixteen juillet 1992

R. BRYANT : Classical, extraordinary and unique holonomies : a standing report
T. SHIOYA : habit of maximal geodesics in Riemannian planes
L. VALERE-BOUCHE : Geodesics in subriemannian singular geometry and control
theory
D. GROMOLL : optimistic Ricci curvature : a few contemporary developements
Ph. DELANOE : Ni’s thesis revisited
E. HEBEY : From the Yamabe challenge to the equivariant Yamabe problem
Vendredi 17 juillet 1992
W. BALLMANN : Brownian movement, Harmonic capabilities and Martin boundary
U. ABRESCH : Graph manifolds, ends of negatively curved areas and the hyperbolic
120-cell space
N. KOISO : Elastica
Jerry KAZDAN : Why a few differential equations don't have any solutions
J. P. BOURGUIGNON : challenge session

2. at the contributions

Among the above pointed out meetings, 5 aren't reproduced in those notes,
namely these by means of Christopher CROKE, Detlef GROMOLL, Jerry KAZDAN, Ren´e
MICHEL and Gilles ROBERT.

Some of them were released in other places, particularly :

CROKE, KLEINER :
Conjugacy and pressure for manifolds with a parallel vector field
J. Differential Geom. 39 (1994), 659-680.
LE COUTURIER, ROBERT :
Lp pinching and the geometry of compact Riemannian manifolds
Comment. Math. Helvetici sixty nine (1994), 249-271.
On the opposite hand, Professor SHIOHAMA, who used to be invited to offer a conversation, had
not been capable of come to the desk Ronde. He sought after however to give a
contribution to Marcel Berger. it's been further to this quantity.

Show description

Commutative algebra, with a view toward algebraic geometry by David Eisenbud

By David Eisenbud

Commutative Algebra is better understood with wisdom of the geometric rules that experience performed a very good function in its formation, briefly, with a view in the direction of algebraic geometry. the writer provides a complete view of commutative algebra, from fundamentals, similar to localization and first decomposition, via size concept, differentials, homological equipment, loose resolutions and duality, emphasizing the origins of the guidelines and their connections with different components of arithmetic. Many routines illustrate and sharpen the idea and prolonged workouts provide the reader an lively half in complementing the fabric offered within the textual content. One novel characteristic is a bankruptcy dedicated to a brief yet thorough therapy of Grobner foundation concept and the optimistic equipment in commutative algebra and algebraic geometry that stream from it. purposes of the idea or even feedback for computing device algebra tasks are incorporated. This booklet will attract readers from novices to complex scholars of commutative algebra or algebraic geometry. to assist newbies, the basic beliefs from algebraic geometry are handled from scratch. Appendices on homological algebra, multilinear algebra and a number of other invaluable subject matters support to make the publication particularly self- contained. Novel effects and shows are scattered in the course of the textual content.

Show description