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.
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 firstname.lastname@example.org, (or John Hunton email@example.com or Nige Ray firstname.lastname@example.org) if you are interested, so we can make approximately the right amount of tea and coffee.