By C. Allday, V. Puppe (auth.), Stefan Jackowski, Bob Oliver, Krzystof Pawałowski (eds.)

ISBN-10: 354047403X

ISBN-13: 9783540474036

ISBN-10: 3540540989

ISBN-13: 9783540540984

As a part of the clinical job in reference to the seventieth birthday of the Adam Mickiewicz collage in Poznan, a world convention on algebraic topology used to be held. within the ensuing court cases quantity, the emphasis is on vast survey papers, a few awarded on the convention, a few written subsequently.

**Read Online or Download Algebraic Topology Poznań 1989: Proceedings of a Conference held in Poznań, Poland, June 22–27, 1989 PDF**

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**Additional resources for Algebraic Topology Poznań 1989: Proceedings of a Conference held in Poznań, Poland, June 22–27, 1989**

**Sample text**

T. Petrie: G-maps and the projective class group, Comment. Math. Helv. 51 (1976), 611626. 44. F. Quinn: Ends of maps, II, Invent. Math. 68 (1982), 353-424. 45. A. Ranicki: The algebraic theory of finiteness obstruction, Math. Scand. 57 (1985), 105-126. 46. C. D. thesis, Princeton 1965. 47. M. Steinberger: The equivariant topological s-cobordism theorem, lhvent. Math. 91 (1988), 61-104. 48. M. E. West: Equivariant h-cobordisms and finiteness obstructions, Bull. Amer. Math. Soc. 12 (1985), 217-220.

Example B(G) Given a topological group G, whose underlying space is a countable C W complex, the following model for the classifying space of G, B( G ), was given in a paper of Milnor [Mi2]. ted join of G with itself, where G is taken n + l times. This is n G space, with diagonal G action on the G coordinates of the join, and orbit space Bn(G). In the case that the underlying space G has the homotopy type of a countable CW complex, the same is true for E , ( G ) and B,,(G). The projection map ha(G) : E , ( G ) ------*B , ( G ) is a fibration with fiber G.

In [J1] he established his model J X for flEX, discussed before in CS10. Using this model he defined in [J2] for each ~' the maps Ck : J X ----* J(X^k), where A ^k is the kD smash power of A, and called those 1naps combinatorial extensions. In particular C2 is a map J X ~ J ( X 2 ). f, a(,f) : A ----* f t ~ X , composing it with the k th combinatorial extension nmp, giving the composition A ~ f~EX ~ flEX ^" and then adjointing back again giving H k ( f ) : E A E X ^~. Thus not only that James' H2 extends Whiteheads' definition (up to sign) of the operator H h)r any dimension q mxd fox' every space X (giving Whiteheads ~ case as a sphere), also the other H~, called nowadays the higher James Hapf Invarianta were introduced by Janms.

### Algebraic Topology Poznań 1989: Proceedings of a Conference held in Poznań, Poland, June 22–27, 1989 by C. Allday, V. Puppe (auth.), Stefan Jackowski, Bob Oliver, Krzystof Pawałowski (eds.)

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