Ninety Second Meeting of the
Transpennine Topology Triangle


School of Mathematics and Statistics

University of Sheffield

Thursday 17th July 2014


Supported by the London Mathematical Society 



Everyone who wishes to participate is welcome, particularly postgraduate students. We'll operate the usual criteria for assistance with travel expenses. Beneficiaries will need to complete the standard forms, available from the TTT Homepage.

Programme

Tea and coffee will be in the common room on I floor of the Hicks Building, on Hounsfield Road. 
All the talks will be in J11 (the usual seminar room on J floor of the Hicks Building).


10:30 – 11:00

Tea, Coffee and Biscuits

11:00 – 12:00 

J11

John Greenlees
(Sheffield)

Ausoni-Bokstedt duality for topological Hochchsild homology.

Calculations of Ausoni, Bokstedt and others show very striking Gorenstein duality
in the topological Hochschild homology of local rings if we take coefficients in the residue field of characteristic p. The purpose of this talk is to give a non-calculational duality statement covering these and many other examples.

This uses the machinery of Gorenstein duality for ring spectra (Dwyer-Greenlees-Iyengar). The only calculational input is Bokstedt's calculation of THH(k) for a field k of characteristic p. Gorenstein ascent is then applied to a cofibration of commutative ring spectra proved by Dundas.

Previous examples of Gorenstein duality ultimately stem (ie via Morita theory
and ascent) from (i) Poincare duality  for manifolds or (ii) Frobenius duality for
group rings, so this does seem to be a new class of examples.

14:00 – 15:00 

J11

Patrick Orson
(Edinburgh)

Double L-theory and localisation

I will give an introduction to the chain complex methods of symmetric algebraic L-theory; a way of algebraically modelling the symmetric properties of topological manifolds, such as Poincare duality, and manifold cobordism. I will describe how I have applied these techniques to the study of the 'doubly-slice' problem in high-dimensional knot theory, by defining an algebraic 'double-cobordism' relation. This new algebra admits a localisation exact sequence which I will describe and compare to the classical Witt group and L-group localisation exact sequences of Milnor-Husemoller and Vogel-Ranicki.

15:00 – 16:00

Tea, Coffee and Biscuits
16:00 –17:00 
J11
Andy Baker
(Glasgow)

Power operations in completed K-theory

 

I will describe the action of power operations on the p-completed K -theory cooperation algebra K^*(K). If times permits I’ll discuss some applications.


There are various places for lunch - follow a group of locals if in doubt.

A group is likely to be going for drinks and an early dinner after the last talk - all are welcome to join.