弦拓扑与环同调

所属分类:数学  
出版时间:2011-6   出版时间:科学出版社   作者:科恩(Ralph L.Cohen)^Kathryn Hess^Alexander A.Voronov   页数:163  

内容概要

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.

作者简介

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

书籍目录

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 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

章节摘录

版权页:插图: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.

图书封面


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用户评论 (总计1条)

 
 

  •     早都复印了一本看. 不过有也比没有好. 本书是分两部分的专著,不厚,但读起来慢.
 

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