Seminario de Álgebra: “Simple groups separated by homological finiteness properties”.- Jueves 18 de junio

El jueves 18 de junio de 2026 tendrá lugar un nuevo Seminario de Álgebra, con la conferencia de título “Simple groups separated by homological finiteness properties” impartida por Claudio Llosa Isenrich (University of Luxembourg). Se celebrará a las 12:00 h en el Seminario de Álgebra, situado en el Edificio B (Matemáticas).

Resumen (en inglés, con símbolos LaTeX):

A group is simple if it has no non-trivial quotients. Simple groups have long played a distinguished role in group theory. Recently, the geometry of simple groups and their finiteness properties have received a lot of attention, for instance through their role in the Boone--Higman Conjecture. The homotopical finiteness properties $F_n$ and the homological finiteness properties $FP_n(R)$, where $R$ is a unital abelian ring, generalize finite generation (which is equivalent to both $F_1$ and $FP_1(R) for any $R$) and finite presentability (which is equivalent to $F_2$). Skipper, Witzel and Zaremsky proved that for every $n\geq 0$ there is a simple group of type $F_n$ and not $F_{n+1}$. This raises the question of how varied the homological finiteness properties of infinitely presented simple groups can be. In this talk, I will explain a construction of examples of simple groups with the same homotopical and homological finiteness properties as Bestvina—Brady groups. In particular, our examples imply the existence of a simple group of type $FP_2(\mathbb{Z})$ which is not finitely presented, answering a question of Zaremsky. This is joint work with Eduard Schesler and Xiaolei Wu.