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Forest-skein groups II: Construction from homogeneously presented monoids

School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia

https://doi.org/10.1142/S0129167X23500428Cited by:0 (Source: Crossref)

Abstract

Inspired by the reconstruction program of conformal field theories of Vaughan Jones we recently introduced a vast class of the so-called forest-skein groups. They are built from a skein presentation: a set of colors and a set of pairs of colored trees. Each nice skein presentation produces four groups similar to Richard Thompson’s group $F, T, V$ and the braided version $B V$ of Brin and Dehornoy.

In this paper, we consider forest-skein groups obtained from one-dimensional skein presentations; the data of a homogeneous monoid presentation. We decompose these groups as wreath products. This permits to classify them up to isomorphisms. Moreover, we prove that a number of properties of the fraction group of the monoid pass through the forest-skein groups such as the Haagerup property, homological and topological finiteness properties, and orderability.

Communicated by Yasuyuki Kawahigashi

Keywords:

AMSC: 20F38, 20F69

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