弦拓撲與環同調（影印版） [String Topology and Cyclic Homology] pdf epub mobi txt 电子书 下载 2025

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[美] 科恩（Ralph L.Cohen） 等 著

圖書標籤:

• 弦拓撲
• 環同調
• 代數拓撲
• 同調代數
• 數學
• 影印版
• 學術著作
• 高等教育
• 專業書籍
• 拓撲學

出版社： 科学出版社

ISBN：9787030313829

版次：1

商品编码：10790855

包装：精装

丛书名： 国外数学名著系列

外文名称：String Topology and Cyclic Homology

开本：16开

出版时间：2011-06-01

用纸：胶版纸

页数：163

字数：205000

正文语种：英文

內容簡介

《弦拓撲與環同調（影印版）》的兩部分分彆介紹StringTopology與CyclicHomology，都是十幾年來代數拓撲學中的新發展，freeloopspace都在其中起著中心作用。屬於“反映學術前沿進展的優秀學術著作”這一類。比較專門，對象是研究生。

目錄

Foreword
I Notes on String Topology
Ralph L.Cohen and Alexander A.Vronov
Introduction
l Intersection theory in loop spaces
1.1 Intersections in compact manifolds
1.2 The Chas-Sullivan loop product
1.3 The BV structure and the string bracket
1.4 A stable homotopy point of view
1.5 Relation to Hochschild cohomology

2 The cacti operad
2.1 PROPs and operads
2.1.1 PROP’S
2.1.2 Algebras over a PROP
2.1.3 Operads
2.1.4 Algebras over an operad
2.1.5 Operads via generators and relations
2.2 The cacti operad
2.3 The cacti action on the loop space
2.3.1 Action via cOrrespOndences
2.3.2 The BV structure

3 String topology as field theory
3.1 Field theories
3.1.1 Topological Field Theories
3.1.2(Topological)Conformal Field Theories
3.1.3 Examples
3.1.4 Motivic TCFTs
3.2 Generalized string topology operations
3.3 Open-closed string topology

4 A Morse theoretic viewpoint
4.1 Cylindrical gradient graph flows
4.2 Cylindrical holomorphic curves in T*M

5 Brahe topology
5.1 The higher-dimensional cacti operad
5.2 The cacti action on the sphere space
5.3 The algebraic structure on homology
5.4 Sphere spaces and Hochschild homology
Bibliography

II An Algebraic Model for Mod 2 Topological Cyclic Homology
Kathryn He88
Preface
1 Preliminaries
1.1 Elementary definitions，terminology and notation
1.2 The canonical，enriched Adams-Hilton model
1.2.1 Twisting cochains
1.2.2 Strongly homotopy coalgebra and comodule maps
1.2.3 The canonical Adams-Hilton model
1.3 Noncommutative algebraic models of fiber squares

2 Free loop spaces
2.1 A simplicial model for the free loop space
2.1.1 The general model
2.1.2 Choosing the free loop model functorially
2.2 The multiplicative free loop space model
2.2.1 The diagonal map
2.2.2 The path fibration
2.2.3 The free loop space model
2.3 The free loop model for topological spaces
2.4 Linearization of the free loop model

3 Homotopy orbit spaces
3.1 A special family of primitives
3.2 A useful resolution of CU*ES1
3.3 Modeling S1 homotopy orbits
3.4 The case of the free loop space
……

前言/序言

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