Transpennine Topology Triangle

Alan Turing Building

University of Manchester

Friday 23 May 2014

The talks will take place in the Frank Adams Seminar Rooms 1 and 2, on the first floor of the Alan Turing Building. The building is number 46 on the University Campus map.

Since 24--26 May is a bank holiday weekend, please note that the schedule is designed to help those who might wish to leave earlier than usual. Others are welcome to stay behind for dinner afterwards.

Participants will meet for coffee from 1100AM onwards in the Atrium Bridge Common Room.

By popular demand, the meeting includes **An afternoon with the
mod 2 Steenrod Algebra**, which will be aimed at those who know little
about the subject, but would enjoy an introduction and a progress report
from two experts who are busy writing a definitive new treatment. They
will welcome questions about the book, as well as the mathematics!

- 11.00-11.30: COFFEE (Atrium Bridge)

- 11.30-12.30: Tara Holm (Cornell University, visiting Oxford)

**The topology of toric origami manifolds**

*A***folded symplectic form**on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the**origami manifolds**. In the classical case, toric symplectic manifolds can classified by their moment polytope, and their topology (equivariant cohomology) can be read directly from the polytope. In this talk we examine the toric origami case: we will recall how toric origami manifolds can also be classified by their combinatorial moment data, and present some theorems, almost-theorems, and conjectures about the topology of toric origami manifolds. - 12.30-2.00: LUNCH

- 2.00-2.45: Reg Wood (Manchester)

**Introduction to the Steenrod algbera 1**

*I shall provide an introduction to the Steenrod squares*Sq^{k}*as operations on polynomials over F*_{2}, as well as to the**hit problem**and to the**conjugate squaring operations**Xq^{k}. - 2.45-3.00: TEA BREAK (Atrium Bridge)

- 3.00-3.45: Grant Walker (Manchester)

**Introduction to the Steenrod algebra 2**

*I will talk about the mod 2 Steenrod algebra as defined by generators Sq*^{k}and the**Adem relations**, and relate this to the setup described in talk 1. I will discuss some of the internal structure, such as**admissible**,**Milnor**and maybe some other bases,**conjugation**, exchanging Sq^{k}and Xq^{k}, and maybe certain**subalgebras**.

Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criterea for assistance with travel expenses, but beneficiaries will need to complete the standard forms, which are available at the TTT Homepage.

Please send a short email to nigel.ray(at)manchester.ac.uk if you expect to attend, so that we can cater for appropriate numbers.

The meeting is jointly supported by the London Mathematical Society and MIMS.