Topology Seminar
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Mon, 16/01/2012 15:45 |
Richard Hepworth (Aberdeen) |
Topology Seminar  |
L3 |
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Chataur and Menichi showed that the homology of the free loop space of the classifying space of a compact Lie group admits a rich algebraic structure: It is part of a homological field theory, and so admits operations parametrised by the homology of mapping class groups. I will present a new construction of this field theory that improves on the original in several ways: It enlarges the family of admissible Lie groups. It extends the field theory to an open-closed one. And most importantly, it allows for the construction of co-units in the theory. This is joint work with Anssi Lahtinen. |
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Mon, 23/01/2012 15:45 |
Gerald Besson |
Topology Seminar |
L3 |
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Mon, 30/01/2012 15:45 |
Chris Cashen |
Topology Seminar |
L3 |
| I will discuss quasi-isometries of the free group that preserve an equivariant pattern of lines. There is a type of boundary at infinity whose topology determines how flexible such a line pattern is. For sufficiently complicated patterns I use this boundary to define a new metric on the free group with the property that the only pattern preserving quasi-isometries are actually isometries. | |||
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Mon, 06/02/2012 03:45 |
Ian Leary (Southampton) |
Topology Seminar |
L3 |
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The Eilenberg-Ganea conjecture is the statement that every group of cohomological dimension two admits a two-dimensional classifying space. This problem is unsolved after 50 years. I shall discuss the background to this question and negative answers to some other related questions. This includes recent joint work with Martin Fluch. |
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Mon, 06/02/2012 13:00 |
Ruth Charney (Brandeis) |
Topology Seminar |
L3 |
| Morgan and Culler proved in the 1980’s that a minimal action of a free group on a tree is completely determined by its length function. This theorem has been of fundamental importance in the study of automorphisms of free groups. In particular, it gives rise to a compactification of Culler-Vogtmann's Outer Space. We prove a 2-dimensional analogue of this theorem for right-angled Artin groups acting on CAT(0) rectangle complexes. (Joint work with M. Margolis) | |||
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Mon, 13/02/2012 15:45 |
Karen Vogtmann (Cornell) |
Topology Seminar |
L3 |
| Free groups, free abelian groups and fundamental groups of closed orientable surfaces are the most basic and well-understood examples of infinite discrete groups. The automorphism groups of these groups, in contrast, are some of the most complex and intriguing groups in all of mathematics. In these lectures I will concentrate on groups of automorphisms of free groups, while drawing analogies with the general linear group over the integers and surface mapping class groups. I will explain modern techniques for studying automorphism groups of free groups, which include a mixture of topological, algebraic and geometric methods. | |||
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Mon, 20/02/2012 15:45 |
Dawid Kielak (Oxford) |
Topology Seminar |
L3 |
For a fixed n we will investigate homomorphisms Out(F_n) to
Out(F_m) (i.e. free representations) and Out(F_n) to
GL_m(K) (i.e. K-linear representations). We will
completely classify both kinds of representations (at least for suitable
fields K) for a range of values  . |
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Mon, 27/02/2012 15:45 |
Ieke Moerdijk (Utrecht and Sheffield) |
Topology Seminar |
L3 |
| I will discuss some aspects of the simplicial theory of infinity-categories which originates with Boardman and Vogt, and has recently been developed by Joyal, Lurie and others. The main purpose of the talk will be to present an extension of this theory which covers infinity-operads. It is based on a modification of the notion of simplicial set, called 'dendroidal set'. One of the main results is that the category of dendroidal sets carries a monoidal Quillen model structure, in which the fibrant objects are precisely the infinity operads,and which contains the Joyal model structure for infinity-categories as a full subcategory. (The lecture will be mainly based on joint work with Denis-Charles Cisinski.) | |||
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Mon, 05/03/2012 15:45 |
Andy Tonks (London Metropolitan University) |
Topology Seminar |
L3 |
The classical associahedra are cell complexes, in fact polytopes,
introduced by Stasheff to parametrize the multivariate operations
naturally occurring on loop spaces of connected spaces.
They form a topological operad  (which provides a resolution
of the operad  governing spaces-with-associative-multiplication)
and the complexes of cellular chains on the associahedra form a dg
operad governing  -algebras (that is, a resolution of the
operad governing associative algebras).
In classical applications it was not necessary to consider units for
multiplication, or it was assumed units were strict. The introduction
of non-strict units into the picture was considerably harder:
Fukaya-Ono-Oh-Ohta introduced homotopy units for -algebras in
their work on Lagrangian intersection Floer theory, and equivalent
descriptions of the dg operad for homotopy unital -algebras
have now been given, for example, by Lyubashenko and by Milles-Hirsch.
In this talk we present the "missing link": a cellular topological
operad  of "unital associahedra", providing a resolution
for the operad governing topological monoids, such that the cellular
chains on is precisely the dg operad of
Fukaya-Ono-Oh-Ohta.
(joint work with Fernando Muro, arxiv:1110.1959, to appear Forum Math) |
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