Download Algebraic Topology, Poznan 1989: Proceedings of a Conference by S. Jackowski, B. Oliver, K. Pawaloski PDF

By S. Jackowski, B. Oliver, K. Pawaloski

As a part of the clinical task in reference to the seventieth birthday of the Adam Mickiewicz college in Poznan, a global convention on algebraic topology was once held. within the ensuing complaints quantity, the emphasis is on titanic survey papers, a few offered on the convention, a few written therefore.

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Extra info for Algebraic Topology, Poznan 1989: Proceedings of a Conference Held in Poznan, Poland, June 22-27, 1989

Example text

Moreover, if the G-end g has a G-collar then it is tame and wH(M,g) ----0 . Now one can formulate the following version of Siebenmann's boundary theorem for smooth G-manifolds. Theorem. 5 Let G be a finite group and M a smooth G-manlfold with one G-end ~. e. if ~ w~(M,~) = ~ ~ then dim ~ - dim M~ 0 for each element [ M H ] of the set CI(M) . If dim MH~ >_ 6 >_ 3 . Let ~ be tame and then there exists a G-collar around the end ~. 7. 5 can be found in [3]. Another particular case of the equivariant boundary theorem for actions on Euclidean spaces was established by A.

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.

The first and the last of those three, are the same for All bundles as they are smaslaes of a map fl'om the base with T(*). Only the middle factor does depend substantiaUy on (. Ganea in [Ga], which is called the Ganea Hopf Invariant of fi. p o' : Bn ~ B ( G ) classifying ~. c~or is T(*) smashed with the evaluation map eA : EFtEA~ -----4EA,. TS5-Exalnples The following are examples for the application of the theorem mentioned in TS4. Example J, (~P) 44 In the case that B = B , = J , ( E P ) , the n th stage in the James model for QE2P, as defined in CS4, it is shown in [D, II, §4] that there is an element ~1 in the image of J (as defined by Hanks) sudh that all pi-2 o T(wi), for 1 < i < n, can be presented as a sum of elements, each ~f :which is a composition A o #, where p is obtained by smashing ~l with tm identity map of ~he space P 4- P , .

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