弦拓?fù)渑c環(huán)同調(diào)

內(nèi)容概要

This book explores string topology,
Hochschild and cyclic homology, assembling material from a wide
scattering of scholarly sources in a single practical volume. The
first part offers a thorough and elegant exposition of various
approaches to string topology and the ChasSullivan loop product.
The second gives a complete and clear construction of an algebraic
model for computing topological cyclic homology.

作者簡(jiǎn)介

作者：（美國(guó)）科恩（Ralph L.Cohen） （美國(guó)）Kathryn Hess （美國(guó)）Alexander A.Voronov

書(shū)籍目錄

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 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 hess
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
 4 a model for mod 2 topological cyclic homology
 4.1 the pth-power map
 4.2 topological cyclic homology
 bibliography

章節(jié)摘錄

版權(quán)頁(yè)：插圖：Thebiholomorphic maps are part of the data, which in particular means that choosinga different biholomorphic map for the same hole is likely to change the point inthe moduli space. The more precise nonoverlapping condition is that the closeddisks in the inputs do not intersect pairwise and the closed disks in the outputs donot intersect pairwise, however, an input and an output disk may have commonboundary, but are still not allowed to intersect at an interior point. This techni-cality brings in the identity morphisms to the PROP, but does not create singularRiemann surfaces by composition. The composition of morphisms in this PROPis given by sewing the Riemann surfaces along the boundaries, using the equationzw = 1 in the holomorphic parameters coming from the standard one on the unitdisk. The tensor product of morphisms is the disjoint union. This PROP plays acrucial role in Conformal Field Theory, as we will see now.

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