On definable subgroups of the fundamental group

Samuel M. Corson

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arXiv · 1610.00145

On definable subgroups of the fundamental group

Samuel M. Corson

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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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Samuel M. Corson. 2016-10-01. On definable subgroups of the fundamental group. https://arxiv.org/abs/1610.00145

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