Topology Seminars Autumn 2010

Monday 20 September
2010 Complexanalytic structures on momentangle manifolds
Taras Panov (Moscow State University)
4pm in FRANK ADAMS 2Abstract (click to view) 
Monday 27 September
2010 (Algebraic) duality in algebraic topology
Francis Clarke (University of Swansea)
4pm in FRANK ADAMS 2Abstract (click to view) 
Monday 04 October
2010 An introduction to quoric manifolds
Jerry Hopkinson (Manchester)
4pm in FRANK ADAMS 2Abstract (click to view)Toric topology has so far been based on the complex numbers and the compact torus. I shall review the basic constructions, and show how to extend the theory to the quaternions and 3spheres, to obtain quoric manifolds. The noncommutativity of the quaternions forces many differences in the details of the constructions, but the classification of these manifolds and the calculation of their cohomology turns out to be closely related to the toric case.

Monday 11 October
2010 Higher categories and configuration spaces
Richard Hepworth (University of Copenhagen)
4pm in FRANK ADAMS 2Abstract (click to view)Joyal introduced categories Theta_n in order to define a theory of weak ncategories. These Theta_n also appear in Rezk's recent approach to the same question. This talk will report on joint work with David Ayala, where we show how the Theta_n encode combinatorial models for configuration spaces of points in R^n. If time permits then I will describe some ambitions regarding Lurie's topological chiral homology.

Monday 18 October
2010 Quasitoric spaces and complex cobordism
Stephen Miller (Manchester)
4pm in FRANK ADAMS 2Abstract (click to view)A quasitoric manifold is a 2ndimensional manifold with an action of the ndimensional torus, such that the orbit space can be identified combinatorially with a simple polytope. Every quasitoric manifold admits a number of stably complex structures compatible with the torus action, and indeed it is known that for n>1 every complex cobordism class contains a quasitoric manifold. The problem of how to compute the cobordism class of a given quasitoric manifold still remains though. By expanding our class of quasitoric spaces, it is possible to construct a quasitoric space which is a final object in an appropriate category. The cohomology of this space is closely related to the cohomology of quasitoric manifolds, and I will show how we can use this tool to address the problem above. The result is an algorithm which involves the simplicial cohomology of a certain (n1)dimensional simplicial complex.

Monday 25 October
2010 The GromovLawsonRosenberg conjecture
Arjun Mulhotra (University of Sheffield)
4pm in FRANK ADAMS 2Abstract (click to view)The GromovLawsonRosenberg conjecture says that a compact manifold with fundamental group G admits a positive scalar curvature metric if and only if a certain topological obstruction vanishes. I will discuss the conjecture and sketch how to prove it for some finite groups.

Monday 01 November
2010 No Seminar (reading week)
Abstract (click to view) 
Monday 15 November
2010 No Seminar (room in use)
Abstract (click to view) 
Monday 22 November
2010 Torus manifolds with nonabelian symmetries
Michael Wiemeler (Manchester)
4pm in FRANK ADAMS 2Abstract (click to view)Let G be a compact connected nonabelian Liegroup and T its maximal torus. A torus manifold with Gaction is defined to be a smooth connected closed oriented manifold M of dimension 2dimT with an almost effective action of G that has nonempty fixed point set. We will discuss the classification of torus manifolds with Gaction up to Gequivariant diffeomorphism.

Monday 29 November
2010 Applications of toric topology to cobordism theory
Nigel Ray (Manchester)
4pm in FRANK ADAMS 2Abstract (click to view)I shall start with the basic ideas of complex cobordism, and attempt to explain how various aspects of the theory may be enriched by importing quasitoric manifolds. I hope to reach a description of the universal toric genus, as developed in work with Taras Panov and Victor Buchstaber (see http://eprints.ma.man.ac.uk/1301/01/covered/MIMS_ep2009_90.pdf).

Monday 06 December
2010 No Seminar (Visit of International Review Panel)
Abstract (click to view) 
Monday 13 December
2010 Fixed point sets and equivariant cell structures for equivariant projective spaces
Gareth Williams (Open University)
Abstract (click to view)Many spaces can be assembled from standard building blocks. These “ cell structures” often permit convenient computation of topological invariants. This lecture highlights the equivariant analogue, for some equivariant projective spaces. The focus will be on pictures, rather than theorems or applications. We shall be concerned mainly with finite, nonabelian groups.
Further information
For further information please contact the seminar organiser.