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Computing the fundamental group of a higher-rank graph

Journal Article


Abstract


  • We compute a presentation of the fundamental group of a higher-rank graph

    using a coloured graph description of higher-rank graphs developed by the third

    author. We compute the fundamental groups of several examples from the

    literature. Our results fit naturally into the suite of known geometrical

    results about $k$-graphs when we show that the abelianisation of fundamental

    group is the homology group. We end with a calculation which gives a

    non-standard presentation of the fundamental group of the Klein bottle to the

    one normally found in the literature.

Publication Date


  • 2013

Citation


  • Kang, S., Pask, D., & Webster, S. B. G. (2013). Computing the fundamental group of a higher-rank graph. Retrieved from http://arxiv.org/abs/1310.7651v3

Web Of Science Accession Number


Abstract


  • We compute a presentation of the fundamental group of a higher-rank graph

    using a coloured graph description of higher-rank graphs developed by the third

    author. We compute the fundamental groups of several examples from the

    literature. Our results fit naturally into the suite of known geometrical

    results about $k$-graphs when we show that the abelianisation of fundamental

    group is the homology group. We end with a calculation which gives a

    non-standard presentation of the fundamental group of the Klein bottle to the

    one normally found in the literature.

Publication Date


  • 2013

Citation


  • Kang, S., Pask, D., & Webster, S. B. G. (2013). Computing the fundamental group of a higher-rank graph. Retrieved from http://arxiv.org/abs/1310.7651v3

Web Of Science Accession Number