"Co-meager isomorphism classes in spaces of enumerated groups"
Kunnawalkam Elayavalli, SrivatsavI will present joint work with I. Goldbring and Y. Lodha where we study the space of enumerated groups which is a topological Polish space consisting of enumerations of countable groups. We also study Polish subspaces of this space consisting of groups with desired properties. There is a fundamental problem of existence of co-meager isomorphism classes in these spaces. We settle this problem for a family of subspaces including the space of all countable enumerated groups and the space of all left orderable enumerated groups. Our work crucially uses tools from combinatorial group theory and work of Hodges on model theoretic forcing.