Homotopy Invariant Algebraic Structures on Topological Spaces
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347 J. M. Board man Johns Hopkins University, Baltimore, MD/USA
R. M. Vogt Mathematisches Institut der Universit~t des Saarlandes, Saarbr0cken/BRD
Homotopy Invariant Algebraic Structures on Topological Spaces
Springer-Verlag Berlin.Heidelberg. New York 1973
A M S Subject Classifications (1970): 55-02, 5 5 D 1 0 , 5 5 D 1 5 , 5 5 D 3 5 , 5 5 D 4 5 , 55F35, 18C10, 18C15
I S B N 3-540-06479-6 S p r i n g e r - V e r l a g Berlin • H e i d e l b e r g • N e w Y o r k I S B N 0-387-06479-6 S p r i n g e r - V e r l a g N e w Y o r k • H e i d e l b e r g , Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin • Heidelberg 1973. Library of Congress Catalog Card Number 73-13427. Printed in Germany. Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
TABLE
Introduction Chapter
I
..................................................
Motivation
and a h i s t o r i c a l
I. " D e ~ o o p i n g " 2. A - s p a c e s
via
survey ..................
c~sssifyin~
space
I
construction
2 4
3. A -ma.ps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
5. Some
approach
remarks
2. Free
4. Free
23
......................
27
......................................
27
7. P a r t t y
I. The
......................................
40
and
of PROs
triples
construction theory
3. L i f t i n ~ IV H o m o t o p y
W@
48
of W~
......................
68
theories
...................
for PROs
and P R O P s
72 72
............
76 83
..............................
95
~5-spaces ............................
95
and
the h o m o t o p y
3. H o m o t o p y
invariance
4. R e t a t i n g
Y-maps
6. An e q u i v a t e n e e
equivatences
to W ~ - h o m o m o r p h i s m s
to Y - s p a c e s
of c a t e g o r i e s
invariance
c a t e g o r y .............
and h o m o t o p y
and h ~ - m a p s
from W~-spaces
7. H o m o t o p y
64
.................................
homomorphisms between
.......................
theories for
57
....................................
theorems
2. C o m p o s i t i o n
5. Maps
........................
and PROPs
homogeneous
2. A f i l t r a t i o n
I. Maps
31
...........................................
6. E x a m p % e s
C h a p t e r Ill The bar
theories
....................................
@-spaces
5. S p i n e s
13
....................
theories
3. I n t e r c h a n g e
.............................
on c o m m u t a t i v i t y
II T o p o t o ~ i c a % - a L g e b r a i c I. D e f i n i t i o n s
Chapter
the
V
........................................
4. A d i f
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