Forty-fourth meeting of the Transpennine Topology Triangle

Department of Pure Mathematics
University of Sheffield
Friday, March 19th 2004

This will be a working meeting. There will therefore be the usual time for participant discussion. Talks will take place in Room J11, on the sixth floor of the Hicks Building.


We expect to go to eat nearby, soon after the last talk.


T.Leinster: "Towards the algebraic topology of self-similar spaces?"

Homotopy and homology work well when the spaces concerned are built up by patching together small contractible pieces. On the other hand, they are near-useless for many self-similar spaces (Julia sets of holomorphic maps on Riemann surfaces being an important example). A different kind of local-to-global patching process turns out to be appropriate in that context. I will describe it, use it to give a precise definition of self-similar space, and explain the surprising result that every compact metrizable space is self-similar. Finally, I will indicate how one day this might give suitable algebraic invariants of self-similar spaces to substitute for homotopy and homology.

S.Theriault: ``The H-structure of low rank torsion free H-spaces.''

Start with a fixed prime p and a space X of t odd dimensional cells, where t is less than p-1. After localizing at p, Cooke, Harper, and Zabrodsky constructed a finite H-space Y with the property that the mod-p homology of Y is generated as an exterior Hopf algebra by the reduced mod-p homology of X. Cohen and Neisendorfer, and later Selick and Wu, reproduced this result with different constructions. We use Selick and Wu's approach to show that Y is homotopy associative and homotopy commutative if X is a suspension and t is less than p-2. Interesting examples include some of the mod-p Stiefel manifolds considered by Mimura, Nishida, and Toda.

John Hunton: "Mayer Vietoris in K-theory"

Suppose Y is a space composed by gluing together some other spaces. I will attempt to relate the resulting K-theories. Complications will ensue as time allows.

Anyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses. We expect to assemble for tea and coffee in I15, Floor 5, from 11.00 am until the first talk. Each lecture will take place in Room J11 of the Hicks Building, Hounsfield Road, Sheffield.
Tea and Coffee will be served in the common room I15.
For further information email John Greenlees, (or John Hunton or Nige Ray if you are interested, so we can make approximately the right amount of tea and coffee.

How to get there

From the rail station, you can catch the Number 60 bus, and get off where it crosses the ring road. Or take the supertram to the University stop. There is more information at School of Mathematics and Statistics Homepage
The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

Escape routes

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