Geometric presentations for Thompson's groups

By Patrick Dehornoy. 2004

52 citations recorded by the source corpus.

We prove that Thompson's groups $F$ and $V$ are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of $F$ and $V$. These presentations lead to considering a certain subgroup of~$V$ and an extension of this subgroup. We prove that the latter are the geometry groups of associativity together with the law $x(yz) = y(xz)$, and of associativity together with a twisted version of this law involving self-distributivity, respectively.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c524126813d21dcd5dbc6bb8e8b240d25f82b14

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The group of parenthesized braids (2004, methodology): “The current paper is self-contained in that it requires no knowledge of the above mentioned papers (by contrast, [ 18 ] resorts to results from the current paper).”
The algebra of strand splitting. I. A braided version of Thompson's group V (2004, background): “Dehornoy’s motivation is not that removed from ours—he builds the groups as braided versions of structure groups of algebraic identities—but his techniques of construction, analysis, and set of observations about the groups are different.”
A nonamenable finitely presented group of piecewise projective homeomorphisms (2016, background): “Also notice that any ys is conjugate by an element of F to exactly one of y, y0, y1, or y10 (to see uniqueness, observe that whether N0 or N1 are in the closure of the support of g is invariant under conjugation and hence none of y0, y10, and y1 are conjugate to each-other).”
Combinatorial algebra : syntax and semantics (2014, unknown): “What is the identity corresponding to x1 ? For more about connections between F and identities of universal algebras, and other representations of F see [81, 111].”