The Barcelona Topology Workshop 2021 (BaToWo'21) will take place on the 27-28th May, via online.
If you are interested in attending the lectures, register via the following form, to receive the link to connect.

Program

Thursday 27th May

18:15 Clover May (UCLA Mathematics)
Decomposing C_2-equivariant spectra
Zoom link

Friday 28th May

Teams link (use Chrome to open the link if you don't have the app)

10:45 Eva Hoening (Radboud University)
Detecting and describing ramification for structred ring spectra

12:15 Cristina Costoya (Universidade da Coruña)
On the (non) existence of strongly inflexible manifolds

17:00 Oihana Garaialde (Universidad del País Vasco)
A family of finite p-groups satisfying Carlson's depth conjecture

18:15 Jérôme Scherer (EPFL Lausanne)
Floyd's manifold is a conjugation space

Abstracts:

• Cristina Costoya, On the (non) existence of strongly inflexible manifolds

An oriented compact connected d-manifold M is inflexible if it does not admit self-maps of unbounded degree. In addition, if all the maps from any other oriented compact connected d-manifold have bounded degree, then M is said to be strongly inflexible. The existence of inflexible manifolds was established by Arkowitz and Lupton, however no example of simply-connected strongly inflexible manifold is known. In this talk using Sullivan models we present an algorithm to check whether a simply-connected manifold is strongly inflexible and we prove that all, but one, of the known examples of simply-connected inflexible manifolds are non-strongly inflexible. This is a joint work with Vicente Muñoz and Antonio Viruel.

• Oihana Garaialde, A family of finite p-groups satisfying Carlson's depth conjecture

We start this talk by recalling some results and a conjecture due to J.F. Carlson that deals with the depth of cohomology rings of groups. Let p>3 be a prime number and let r be an integer less than p-1. For each r, we later consider the unique quotient of the maximal class pro-p group G_r of size p^{r+1}. We show that the mod-p cohomology ring of G_r has depth one and that, in turn, it satisfies the aforementioned conjecture. The novelty of our result is that we do not have to compute the cohomology rings to deduce their depth. This is a joint work with Jon González-Sánchez and Lander Guerrero Sánchez.

• Eva Hoening, Detecting and describing ramification for structured ring spectra

In this talk we consider the question of how to transfer the classical ramification theory from algebra to structured ring spectra. We discuss examples in the context of topological K-theory and topological modular forms, and use the Tate construction to propose a definition of tame and wild ramification for commutative ring spectra. This is joint work with Birgit Richter.

• Clover May, Decomposing C2-equivariant spectra

Computations in RO(G)-graded Bredon cohomology can be challenging and are not well understood, even for G=C_2, the cyclic group of order two. A recent structure theorem for RO(C_2)-graded cohomology with Z/2 coefficients substantially simplifies computations. The structure theorem says the cohomology of any finite C2-CW complex decomposes as a direct sum of two basic pieces: cohomologies of representation spheres and cohomologies of spheres with the antipodal action. This decomposition lifts to a splitting at the spectrum level. In joint work with Dan Dugger and Christy Hazel we extend this result to a classification of compact modules over the genuine equivariant Eilenberg-MacLane spectrum HZ/2.

• Jérôme Scherer, Floyd’s manifold is a conjugation space

This is joint work with Wolfgang Pitsch. In this talk I’d like to explain how Floyd constructed his famous manifolds with four cells, and refine it to an equivariant construction using Lück and Uribe’s framework for equivariant bundles. Once this is done a characterization obtained in joint work with Ricka and a general splitting result by C. May allows us to conclude that we are dealing indeed with a conjugation manifold as introduced by Hausmann-Holm-Puppe.

Organising Committee: Natàlia Castellana (Universitat Autònoma de Barcelona)