# On definable subgroups of the fundamental group

Source: [On definable subgroups of the fundamental group](<https://www.sota2.com/research/paper/68fa57651e209131ce9a5344>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T14:43:29.035Z

Authors: Samuel M. Corson

Published: 2016-10-01T15:11:18.000Z

## Abstract

We present several new theorems concerning the first fundamental group of a path connected metric space. Among the results proven are strengthenings of the main theorems of \\cite{Sh2} and \\cite{CoCo}. A compactness theorem for the fundamental group of a Peano continuum is given. A useful characterization for the shape kernel of a locally path connected space is presented, along with a very succinct proof of the fact that for such a space the Spanier and shape kernel subgroups coincide (see \\cite{BF}). We also show that a free decomposition of the fundamental group of a locally path connected Polish space cannot be nonconstructive. Numerous other results and examples illustrating the sharpness of our theorems are provided.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1610.00145>)

[PDF](<https://arxiv.org/pdf/1610.00145.pdf>)