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

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

As a part of the medical 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 vast survey papers, a few offered on the convention, a few written hence.

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

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The second section (TS) takes on one of the theorems mentioned in CS, nmnely, the fact that Thorn spaces of bundles over conic bases are conic• Since this is a review paper, the section revmws some older results in the same direction, The third section (HI) reviews the subject of Hopf Invariants. Those Hopf invariants come into the description of the relative attaching maps in Thorn spaces so that some of the constructions in HI are mentioned in TS too, but HI discusses some older constructions.

7 Let V be a G-representation satisfying "gap hypothesis" and with dim VG >_ 5 . Then stab#]zatlon maps ~° \ Pt~(v) ) --* ~o \ Pt~(v • R) ] and { "° \ oa(v) / are (To dL R_)l -~ ~° \ oG(v • R) / onto. 8 Let V and W be as above. Then V ~ R is G-homeomorphlc to W ~ R iff V is G- homeomorphic to W . 9 Let V be a G-representation with dim ~3 > 5 which satisfies a certain "vanishing condition" ( [4~, p. 70 ) in degrees >_ k , where 1 < k < dim VG . Then the space TOPG(V ~ R)/TopG(V ) is (dim V 3 - k)- connected.

The following are three examples of conic (non CI~") presentations. E x a m p l e J,,(EP) Given a space X, the James model for f/EX, denoted J(X), was first considered in [J1], (mid was denoted X¢¢ ). Filtration one is given on X, while the basepoint * of X is given filtration zero. There is an induced filtration on XX,, the n -th cartesiml power of X, and on lira X × ' , denoted X ~ , such that under the induced equivalence relation X ~ / ~ denoted J ( X ) becomes the free monoid on X, mad X × " / ~ denoted J , ( X ) gives a filtration on J ( X ) .

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