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Algebraic Topology Poznań 1989: Proceedings of a Conference by C. Allday, V. Puppe (auth.), Stefan Jackowski, Bob Oliver,

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

As a part of the clinical task in reference to the seventieth birthday of the Adam Mickiewicz collage in Poznan, a global convention on algebraic topology used to be held. within the ensuing complaints quantity, the emphasis is on big survey papers, a few offered on the convention, a few written subsequently.

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Siebenmann: Foundational essays on topological manifolds, smoothlngs and triangulations, Ann. Math. Studies 88 (1977), Princeton Univ. Press. 29. T. C. Ku: Obstruction theory for finite group actions, Osaka J. Math. 18 (1981), 509-523. 30. S. Kwasik: On the equivariant homotopy type of G-ANR's, Proc. Amer. Math. Soc. 267 (1981), 193-194. 31. S. Kwasik: On equivariant finiteness, Compositio Math. 48 (1983), 363-372. 32. S. Kwasik: Locally smooth G-manifolds, Amer. 3. Math. 108 (1986), 27-37. 33.

29 (1982), 27-42. 2. P. Andrzejewski: The equivariant Wall finiteness obstruction and Whitehead torsion, Transformation Groups, Pozna~ 1985, pp. 11-25, Lecture Notes in Math. 1217, Springer Vlg 1986. 3. P. Andrzejewski: An application of equivariant finiteness obstruction equivariant version of Siebenmann's theorem, (preprint, to appear). 4. P. Andrzejewski: A complement to the theory of equlvariant finiteness obstruction (preprint 1989). 5. H. Assadi: Extensions of group actions from submanlfolds of disks and spheres (preprint).

THEOREM A. pace X with all the rood p homology groups finite di: menslonM has the property that the depth of the algebra H . ( ~ X , lp) is not bigger than the Lusternik-Schnilvhnaml category of X . Every finite conic space composed of n cones has Lusternik-Schlfirelmann category lesser than n~ and thus theorem A applies to finite simply connected conic spaces with finite dimensional ~tod p homology groups. CS6-A t h e o r e m about conic spaces 41 THEOREM. A Thorn space of a bundle over a conic space is conic, In this last theorem the %undle' can be a fiber bundle, The Thorn space of the fiber bundle is defined [HS] as the ma,pping cone of the projection map, In the usual case of vector bundles, the associated sphere bundle has a Thorn space in the new defiifition Milch is the same as the classical Thorn complex of the original vector bundle.

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