Forty First Meeting of the Transpennine Topology Triangle

Department of Mathematics
University of Manchester
Monday 20th October 2003

Programme

First talk will be in the Mathematics Tower, Room G14. Two other talks, tea and informal discussion will take place in the Brian Hartley Room, floor 6. We will meet in the BHR for coffee from 1100AM onwards.

Titles and speakers are as follows.

Abstracts

Alastair Hamilton (Bristol)
Title: Deformations of A-infinity algebras
Abstract: Deformations of A-infinity algebras will be considered, focusing in particular on formal one-parameter deformations. A-infinity algebras will be defined via the cobar construction and the resulting effect on the calculations discussed. Hochschild cohomology of an A-infinity algebra will be defined and its relation to deformation theory explained. A type of A-infinity algebra called a Moore algebra will be introduced. These are closely related to the one dimensional A-infinity algebras considered by Kontsevich which generate the Miller-Morita-Mumford classes in the cohomology of moduli spaces of complex algebraic curves.
Slides of talk


Revaz Kurdiani (Aberdeen)
Title: The Leibniz algebra structure on the second tensor power of Lie algebra
Abstract: The notion of Leibniz algebra was introduced not very long time ago, which is a generalization of the notion of Lie algebra. It turns out that the second tensor power of Lie algebra is a Leibniz algebra. My talk will be concentrated on this Leibniz algebra. Namely the elementary properties of this algebra will be stated. Also I will describe the non-abelian second tensor power of Lie algebra constructed by Ellis [J. Pure Appl. Algebra 46(1987), 111--115 and Glasgow Math. J. 33(1991), 101--120] (non-abelian tensor product of groups was introduced by Brown and Loday in [Topology 26(1987), 311--335]). Moreover, the maximal Lie algebra quotient of studied Leibniz algebra is an abelian extension of the non-abelian second tensor power of Lie algebra. For finite dimensional semi-simple Lie algebra the kernel of this extension will be described explicitly.

Andy Tonks (London)
Title: The associahedron diagonal approximation
Abstract: The associahedra, or "Stasheff polytopes", were introduced by Jim Stasheff in 1963 for the study of homotopy associativity of H-spaces. Combinatorially their cells correspond to bracketings or to planar rooted trees, and their vertices are counted by the Catalan numbers. The associahedron diagonal approximation, recently introduced in preprints of Saneblidze and Umble, can be seen as a generalising both the classical (simplicial) Alexander-Whitney diagonal approximation and the obvious cubical diagonal approximation. In this talk I will discuss some geometric and combinatorial aspects of these diagonal approximations, and their relation with loop spaces, cobar constructions, and the Baues conjecture on the homotopy type of certain order complexes.

Lunch will be taken locally (at the vegetarian "On the Eight Day", for example), and we expect to visit a local curry house (or similar) early in the evening.

Everyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses. Please email Nige Ray nige@ma.man.ac.uk (or John Greenlees j.greenlees@sheffield.ac.uk, or John Hunton jrh7@mcs.le.ac.uk) if you are interested in attending, so that we can cater for appropriate numbers.

How to get there

If you need help in finding the Mathematics (the tallest building on Oxford Road!), there is more information at University of Manchester, Department of Mathematics Homepage
The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

Escape routes

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