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On the Fundamental Group of Inverse Limits

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Abstract

In this paper we study the fundamental group of inverse limits, obtained by upper semi-continuous set valued functions. We present a number of crucial examples which demonstrate the technical difficulties, related to the control of the fundamental group in the inverse limit. Furthermore, these examples realize some important groups as the fundamental groups of inverse limits: free groups and the Hawaiian Earring group. On the other hand, we introduce the right shift of a loop in the inverse limit and prove that the fundamental group of an inverse limit, which is a one-dimensional Peano continuum, is often trivial or uncountable.

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Acknowledgments

This research was supported by the Slovenian Research Agency Grants P1-0292-0101 and J1-6721-0101

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, 1000, Ljubljana, Slovenia

    Aleš Vavpetič & Žiga Virk

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  1. Aleš Vavpetič
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  2. Žiga Virk
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Correspondence to Aleš Vavpetič.

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Communicated by Rosihan M. Ali, Dato’.

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Vavpetič, A., Virk, Ž. On the Fundamental Group of Inverse Limits. Bull. Malays. Math. Sci. Soc. 40, 941–957 (2017). https://doi.org/10.1007/s40840-016-0327-1

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  • DOI: https://doi.org/10.1007/s40840-016-0327-1

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