Seventy Fourth Meeting of the Transpennine Topology Triangle

School of Mathematics
Alan Turing Building
University of Manchester
Monday 5th July 2010

Supported by the London Mathematical Society and MIMS

MIMS TTT74 Link

Programme

The talks will take place in the Frank Adams Seminar Rooms 1 and 2, on the first floor of the Alan Turing Building. This is on the east side of the campus, off Upper Brook Street and about 100m south of the junction with Booth Street East. It is about 15 minutes walk from Piccadilly station, through the old UMIST campus and under the Mancunian Way. The building is number 46 on the University Campus map.

Participants will meet for coffee from 1100AM onwards in the Atrium Bridge Common Room; the Frank Adams Rooms open into the common room.

Lunch may be taken in any of several local venues (such as the cafe in the atrium, or the vegetarian "On the Eighth Day", for example), and we expect to visit a nearby restaurant for early-evening dinner.

• 11.00-11.30: COFFEE (Atrium Bridge)
  

• 11.30-12.30: Alex Gonzalez (Sheffield)
  Unstable Adams operations acting on p-local compact groups and fixed points.
  p-local compact groups were recently introduced by C. Broto, R. Levi and B. Oliver as algebraic models for p-completions of classifying spaces of compact Lie groups and p-compact groups. In this new setting, a definition of unstable Adams operations for p-local compact groups was provided in F. Junod, along with a proof of their existence in all cases. We then study the action of such operations on a fixed p-local compact group, and study whether the corresponding fixed points form a p-local finite group. The importance of such a result is great: first, this would provide a unifying statement and proof for results on compact Lie groups and p-compact groups. Also, this would provide a powerful tool to extend known results on p-local finite groups to the compact case. Some examples will be discussed at the end.

• 12.30-2.30: LUNCH
  

• 2.15-3.15: Jeff Giansiracusa (Swansea)
  Modular operads and diffeomorphisms of 3-dimensional handlebodies.
  Configurations spaces of points in the plane form an operad, and configuration spaces of framed points form a cyclic operad (the roles of inputs and outputs can be exchanged). I will describe how the modular operad generated by this cyclic operad gives a model for BDiffs of 3- dimensional handlebodies. This leads to a graph complex computing the cohomology of these BDiffs.

• 4.00-5.00: Ronnie Brown (Bangor)
  Some strict higher homotopy groupoids: intuitions, examples, applications, prospects.
  The aim is to show how the idea of ‘algebraic inverse to subdivision’ led to a family of strict higher homotopy groupoids more intuitive and powerful than the earlier relative homo- topy groups, through having structure in a full range of dimensions and also the advantages of symmetry and multiple compositions. These structures help not only to understand traditional 1 structures of such homotopy groups, such as actions but can allow specific calculations of some such groups through calculation of richer structures, modelling the n-types. Even richer structures allow calculations of say Whitehead products and new results such as an n-adic Hurewicz theorem.

Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criterea for assistance with travel expenses, but beneficiaries will need to complete the standard forms, and should come armed with NI numbers and details of UK bank accounts. Please email nigel.ray(at)manchester.ac.uk if you expect to attend, so that we can cater for appropriate numbers.

The meeting is jointly supported by the London Mathematical Society and MIMS.

Escape routes