On definable subgroups of the fundamental group (Q1738948)

Algebraic invariants of Peano continua and more general path connected metric spaces are challenging objects. Their study has mostly focused on the fundamental group, which turns out to contain a lot of information about the underlying space, especially if the space is one-dimensional. In this paper the author studies fundamental groups and their subgroups from the point of view of descriptive set theory. Results include Theorem A (determining the cardinality of the fundamental group and some of its quotients), Theorem B (non-existence of a strictly increasing infinite sequence of normal subgroups, whose union is the fundamental group), and some other structural results. The author also introduces comonster groups and incorporates them into his results.