One hundred and fourth meeting of the
Transpennine Topology Triangle


University of Sheffield

Thursday 20th July 2017


Supported by the London Mathematical Society


Programme

Talks will be in J11 (J floor) and coffee/tea in the common room I15 (I floor) of the Hicks building. 

10:30 - 11:00
Tea/coffee
11:00 - 12:00

Dae-Woong Lee (Chonbuk, Korea)
On the Steenrod homology, co-Hopf structures, SNT and the Brown-Peterson spectra
12:00 - 14:00
Lunch
14:00 - 15:00

 Dean Barber (Sheffield)
A Combinatorial Model for the Fulton-Macpherson Operads
15:00 - 16:00
Tea/coffee
16:00 - 17:00

Andy Tonks (Leicester)
Tilings, Trees, DG2As and B∞-Algebras

A group is expected to go for drinks and an early dinner after the last talk. Everyone is welcome to join us.

Abstracts of talks

Dean Barber (Sheffield)
Title: A Combinatorial Model for the Fulton-Macpherson Operads
Abstract

Dae-Woong Lee (Chonbuk, Korea)
Title: On the Steenrod homology, co-Hopf structures, SNT and the Brown-Peterson spectra
Abstract:  
In this talk, we describe some fundamental results about the strong (co)homology groups of inverse systems and phantom groups.

We also describe the set of comultiplications on a wedge of finite number of spheres. We are primarily interested in the size of this set and properties of the comultiplications such as associativity and commutativity. Our methods involve Whitehead products in wedges of spheres and the Hopf-Hilton invariants. We apply our results to specific examples and determine the number of comultiplications, associative comultiplications and commutative comultiplications in these cases. This is a part of a joint work with Martin A. Arkowitz.

By using the rational homotopy theory, we give an answer to the question on the same n-type structure based on the infinite complex projective space raised by C.A. McGibbon and J.M. Moller in 1990, and describe the generalized SNT conjectures of CW-complexes. Especially, we show that the set of all the same n-types of the suspension of the Eilenberg-MacLane spaces is the one element set consisting of a single homotopy type.

Finally, we consider the homotopy structure of the Real-oriented Brown-Peterson spectrum and the local cohomology of the basic block and the negative block of the homotopy of BPR<3>, and their Anderson duals. This is a joint work in progress with J.P.C. Greenlees.


Andy Tonks (Leicester)
Title: Tilings, Trees, DG2As and B∞-Algebras

Abstract:
Recall that a B∞-structure may be expressed as a DG bialgebra structure on a cofree coassociative algebra, or as a multibrace algebra with a compatible A∞-structure. Loday and Ronco showed that the primitive part of a cofree Hopf algebra is a multibrace algebra, constructed its universal enveloping 2-associative algebra, and gave descriptions of the free multibrace and 2-associative algebras in terms of trees. In joint work with Gálvez-Carrillo and Ronco we extend these results to B∞ and differential graded 2-associative algebras, and describe the free objects in terms of guillotine partitions in d=3 dimensions.


Everyone who wishes to participate is welcome, particularly postgraduate students. The usual criteria for assistance with travel expenses apply. Beneficiaries will need to complete the standard forms, which are available at the TTT Homepage.