弦拓扑与环同调
作 者： （美）科恩 等编著
出版时间：2011
内容简介
This book explores string topology，Hochschild and cyclic homology， assembling material from a widescattering of scholarly sources in a single practical volume. Thefirst part offers a thorough and elegant exposition of variousapproaches to string topology and the ChasSullivan loop product.The second gives a complete and clear construction of an algebraicmodel for computing topological cyclic homology.
目录
i notes on string topology
ralph l. cohen and alexander a. voronov
introduction
1 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 stringbracket
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 viacorrespondences
2.3.2 the bv structure
3 string topology as field theory
3.1 field theories
3.1.1 topological fieldtheories
3.1.2 (topological) conformal fieldtheories
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 hess
preface
1 preliminaries
1.1 elementary definitions, terminology andnotation
1.2 the canonical, enriched adams-hiltonmodel
1.2.1 twisting cochains
1.2.2 strongly homotopy coalgebraand comodule maps
1.2.3 the canonical adams-hiltonmodel
1.3 noncommutative algebraic models of fibersquares
2 free loop spaces
2.1 a simplicial model for the free loopspace
2.1.1 the general model
2.1.2 choosing the free loop modelfunctorially
2.2 the multiplicative free loop spacemodel
2.2.1 the diagonal map
2.2.2 the path fibration
2.2.3 the free loop spacemodel
2.3 the free loop model for topologicalspaces
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
4 a model for mod 2 topological cyclic homology
4.1 the pth-power map
4.2 topological cyclic homology
bibliography
