Final Schedule, 29th British Topology Meeting

All lectures will take place in the Lecture room A (= room 1041) of the Shackleton Building, which is building 44 near the bottom left corner of this map.

There will be a wine reception on the evening of Monday 8th, jointly with the International Conference on Generalized Functions. This will be held in the Ketley Room on level 4 of the Mathematics Building, which is Building 54 on the top left of on the same map.

For lunch, participants are recommended to visit the Staff Social Club, in Building 38 near the centre of the map.

Monday 8 September
13:00-14:00 Registration
14:00-15:00 Brendle
15:30-16:00 Kaji
Tea
16:30-17:30 Vershinin
18:00-19:00 Wine Reception

Tuesday 9 September
10:00-11:00 Madsen
Coffee
11:30-12:00 Spacil
12:00-12:30 Kurlin
Lunch
14:30-15:00 Beben
15:30-16:00 Huismann
Tea
16:30-17:30 Murillo
19:00 Conference Dinner at Ceno Restaurant.

Wednesday 10 September
10:00-11:00 Richter
Coffee
11:30-12:00 Tene
12:00-13:00 Wilton

Titles and Abstracts

1. Tara Brendle (Glasgow): Combinatorial models for mapping class groups

2. Shizuo Kaji (Yamaguchi and Southampton): Mod-p decompositions of the loop spaces of compact symmetric spaces

Abstract: We give homotopy decompositions of the based loop spaces of compact symmetric spaces after they are localised at large primes. The factors are fairly simple; namely spheres, sphere bundles over spheres, and their loop spaces. As an application, upper bounds for the homotopy exponents are determined. This is a joint work with A. Ohsita and S. Theriault.

3. Vladimir Vershinin (Montpelier 2): Lie algebras and Vassiliev invariants

Abstract: We start with a general construction of the Lie algebra (over the integers) of the descending central series of a group. Then we give presentations for the corresponding Lie algebras for classical braids, for braids on the 2-dimensional sphere and for braids on a surface of arbitrary genus. Finally we give a construction of the universal Vassiliev invariant for braids on a 2-sphere.

4. Ib Madsen (Copenhagen): Real Algebraic K-theory

5. Oldrich Spacil (UCL): Homotopy type of the group of contactomorphisms of the 3-sphere

Abstract: After recalling basic notions of contact topology I will present a simple proof showing that the homotopy type of the group of contactomorphisms of the standard contact 3-sphere is that of the unitary group U(2). The tools used are almost elementary algebraic topology, but the starting line is a hard geometric result of Eliashberg.

6. Vitaliy Kurlin (Durham): Topological Data Analysis: Applications to Computer Vision

Abstract: Topological Data Analysis is a new research area on the interface between algebraic topology, computational geometry, machine learning and statistics. The key aims are to efficiently represent real-life shapes and to measure shapes by using topological invariants such as homology groups. The usual input is a big unstructured point cloud, which is a finite metric space. The desired outputs are persistent topological structures hidden in the given cloud. The flagship method is persistent homology describing the evolution of homology classes in the filtration on the data over all possible scales. After reviewing basic concepts and results, we consider the problem of counting holes in noisy 2D clouds. Such clouds emerge as laser scans of building facades with holes representing windows or doors. We design a fast algorithm to count holes that are most persistent in the filtration of neighborhoods around points in the given cloud. We prove theoretical guarantees when the algorithm finds the correct number of holes (components in the complement) of an unknown shape approximated by a cloud in the plane.

7. Piotr Beben (Southampton): Configuration spaces and polyhedral products

Abstract: We use configuration space models for spaces of maps into certain subcomplexes of product spaces (including polyhedral products) to obtain a single suspension splitting for the loop space of certain polyhedral products, and show that the summands in these splittings have a very direct bearing on the topology of polyhedral products, and moment-angle complexes in particular.

8. Johannes Huisman (Brest): Chern-Stiefel-Whitney classes of real vector bundles

Abstract: Let X be a real algebraic variety and F a real vector bundle over X. I will define Chern-Stiefel-Whitney classes of F with values in certain hypercohomology groups on the quotient topological space X(C)/G, where G is the Galois group of C/R. These classes unify the ordinary characteristic classes in the sense that they induce the Chern classes of F(C), on the one hand, and the Stiefel-Whitney classes of F(R), on the other hand. The construction sheds a seemingly new light on the fact that the mod-2 cohomology ring of a real Grassmannian is the reduction modulo 2 of the integral cohomology ring of a complex Grassmannian after dividing all degrees by 2.

9. Aniceto Murillo (Malaga): Deformation functors and homotoy theory of Lie algebras

Abstract: Having as reference and motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which include the classical Quillen approach.

10. Birgit Richter (Hamburg): Higher topological Hochschild homology of rings of integers.

Abstract: This is a report on joint work in progress with Bj{\o}rn Dundas and Ayelet Lindenstrauss. We calculate higher THH of the integers with coefficients in F_p and also for (certain) rings of integers in a number field. This builds on the calculation of THH in these cases of B\"okstedt and Lindenstrauss-Madsen.

11. Haggai Tene (Bonn): A product in equivariant homology for compact Lie group actions

Abstract: In this talk we present a product in the (Borel) equivariant homology of a smooth manifold with a compact Lie group action. This construction generalizes a product in the homology of BG defined by Kreck. We give some computational results, and relate the product to the product in negative Tate cohomology in the case G is finite and the manifold is a point. This is a joint work with S. Kaji.

12. Henry Wilton (Cambridge): Detecting hyperbolicity in finite covers

Abstract: In practice, one of the most common ways of proving that two closed, aspherical 3-manifolds M, N are distinct is to compare their finite-sheeted covers. An open question in 3-manifold topology asks to what extent this method always works. In more sophisticated terminology, the question asks: 'If the profinite completions of the fundamental groups of M and N are isomorphic, does it follow that M and N are homeomorphic (unless they both admit Solv geometry)?'

In this talk I will report on recent progress towards a positive answer: the profinite completion 'sees' hyperbolicity, in the sense that if M is hyperbolic then so is N. To prove this theorem, we develop a profinite analogue of the quasiconvex hierarchy for hyperbolic 3-manifolds employed by Wise and Agol in their work on the Virtually Fibred conjecture.

This is joint work with Pavel Zalesskii.

Last updated on 3rd September 2014.