書馨卡幫你省薪 2024個人購書報告 2024中圖網年度報告
歡迎光臨中圖網 請 | 注冊
> >
有理同倫論-(影印版)

有理同倫論-(影印版)

作者：菲利克斯
出版社：世界圖書出版公司出版時間：2013-03-01
開本： 24開 頁數(shù)： 535
本類榜單：教材銷量榜
中 圖 價:¥85.1(8.6折) 定價  ¥99.0 登錄后可看到會員價
加入購物車 收藏
運費6元，滿39元免運費
?新疆、西藏除外
本類五星書更多>

有理同倫論-(影印版) 版權信息

  • ISBN：9787510058349
  • 條形碼：9787510058349 ; 978-7-5100-5834-9
  • 裝幀：一般膠版紙
  • 冊數(shù)：暫無
  • 重量：暫無
  • 所屬分類：>

有理同倫論-(影印版) 本書特色

　　r，ational homotopy theory has the disadvantage of discarding a considerable amount of information.  for example， the homotopy groups of the sphere s'2 are non-zero in infinitelv many degrees whereas its rational homotopy groups vanish in all degrees above 3. by contrast， rational homotopy theory has the advantage of being remarkably computational. for example， there is not even a conjectural description of all the homotopy groups of any simply connect.ed finite cw complex， whereas for many of these the rational groups can be explicitly determined.  and while rational homotopy theory is indeed simpler than ordinary homotopy theory， it is exactly this simplicity that makes it possible to address （if not alway-s to solve） a number of fundamental questions.

有理同倫論-(影印版) 內容簡介

本書是講述有理同倫的教材，有該領域的三位知名作者合著而成。同倫理論是代數(shù)拓撲的一個分支，書中講述了該領域的主要定理和完整證明，并將有理同倫理論的表示和技巧做了大量的簡化，書中呈現(xiàn)了許多重要結果的現(xiàn)代證明，這些結果都是十來年的主要貢獻。目次：（一）同倫理論、纖維化結果和P局部空間：拓撲空間；CW復數(shù)，同倫群和上纖維化；纖維化和拓撲獨異點；階化代數(shù)；奇異鏈、同調和Eilenberg-Maclane空間；上鏈代數(shù)C*(X;k)；（R，d）模和半自由解；纖維化的半自由上鏈模；G-纖維化的半自由鏈模；P-局部和有理空間；（二）Sullivan模：空間的交換上鏈代數(shù)和簡化集；光滑微分形式；Sullivan模；黏著空間、同倫群和Whitehead乘積；相對Sullivan代數(shù)；纖維化、同倫群和李群行為；環(huán)空間同倫代數(shù)；空間現(xiàn)實；（三）階化微分代數(shù)：譜序列；階化模的映射解；（四）李模：階化李代數(shù)和Hopf代數(shù)；Quillen因子的C*和￡；交換上鏈代數(shù)；拓撲空間和CW復形；鏈李代數(shù)和拓撲群；dg Hopf代數(shù)；（五）有理Lusternik Schnirelmann范疇；有理LS范疇和有理錐長度；Sullivan代數(shù)的LS范疇；乘積的有理LS范疇和纖維叢；同倫里代數(shù)和完整表示；（六）有理二分：橢圓和雙曲空間和其他應用：橢圓空間；有理同倫群增長；Hochachild-Serre譜序列；纖維和環(huán)空間的分級和深； 有限深李代數(shù)；細胞粘附；Poincare對偶；十七開放問題。

有理同倫論-(影印版) 目錄

Introduction Table of Examples Ⅰ Homotopy Theory, Resolutions for Fibrations, and Plocal Spaces 0 Topological spaces 1 CW complexes, homotopy groups and coflbrations (a) CW complexes (b) Homotopy groups (c) Weak homotopy type (d) Cofibrations and NDR pairs (e) Adjunction spaces (f) Cones, suspensions, joins and smashes 2 Fibrations and topological monoids (a) Fibrations (b) Topological monoids and G-fibrations (c) The homotopy fibre and the holonomy action (d) Fibre bundles and principal bundles (e) Associated bundles, classifying spaces, the Borel construction and the holonomy fibration 3 Graded (differential) algebra (a) Graded modules and complexes (b) Graded algebras (c) Differential graded algebras (d) Graded coalgebras (e) When k is a field 4 Singular chains, homology and Eilenberg-MacLane spaces (a) Basic definitions, (normalized) singular chains (b) Topological products, tensor products and the dgc, C*(X;k) (c) Pairs, excision, homotopy and the Hurewicz homomorphism (d) Weak homotopy equivalences (e) Cellular homology and the Hurewicz theorem (f) Eilenberg-MacLane spaces 5 The cochain algebra C*(X;k) 6 (R,d)-modules and semifree resolutions (a) Semifree models (b) Quasi-isomorphism theorems 7 Semifree cochain models of a flbration 8 Semifree chain models of a G-flbration (a) The chain algebra of a topological monoid (b) Semifree chain models (c) The quasi-isomorphism theorem (d) The Whitehead-Serre theorem 9 p-local and rational spaces (a) p-local spaces (b) Localization (e) Rational homotopy type Ⅱ Sullivan Models Ⅲ Graded Differential Algebra (continued) Ⅳ Lie Models Ⅴ Rational Lusternik Schnirelmann Category Ⅵ The Rational Dichotomy References Index
展開全部

有理同倫論-(影印版) 作者簡介

Yves Félix, Stephen Halperin, Jean-Claude Thomas是國際知名學者，在數(shù)學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用于科研工作者、高校教師和研究生。

商品評論(0條)
暫無評論……
書友推薦
本類暢銷
編輯推薦
返回頂部
中圖網
在線客服