Group Theory

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New submissions for Mon, 13 May 24

[1]  arXiv:2405.06594 [pdf, ps, other]

Title: The homology of completely simple semigroups

Authors: Benjamin Steinberg

Subjects: Group Theory (math.GR)

I explicitly compute the Eilenberg-Mac Lane homology of a completely simple semigroup using topological means. I also complete Gray and Pride's investigation into the homological finiteness properties of completely simple semigroups, as well as studying their topological finiteness properties. I give a topological proof of Pride's unpublished homological lower bound for the deficiency of a monoid or semigroup.

Cross-lists for Mon, 13 May 24

[2]  arXiv:2405.06169 (cross-list from math.GT) [pdf, other]

Title: Left-orderability of Groups Acting on Bifoliated Planes

Authors: Mauro Camargo-Rios, Lingfeng Lu

Comments: 17 pages, 8 figures

Subjects: Geometric Topology (math.GT); Group Theory (math.GR)

We prove that any group acting faithfully on a bifoliated plane while preserving the orientations of both foliations is left-orderable. The proof utilizes a construction of a linear order on the set of ends of the leaf spaces, which takes advantage of the additional structure coming with a bifoliation. Moreover, we build an identification between ends of leaf spaces of the bifoliation and subsets of the boundary circle at infinity, and use it to give a condition for the equivalence between a faithful group action on a bifoliated plane and a faithful group action on the set of ends of the leaf spaces.

[3]  arXiv:2405.06171 (cross-list from math-ph) [pdf, ps, other]

Title: Projective connections and extremal domains for analytic content

Authors: Razvan Teodorescu

Journal-ref: 2019 J. Phys.: Conf. Ser. 1194 012105

Subjects: Mathematical Physics (math-ph); Group Theory (math.GR); Operator Algebras (math.OA); Quantum Physics (quant-ph)

This note expands on the recent proof \cite{ABKT} that the extremal domains for analytic content in two dimensions can only be disks and annuli. This result's unexpected implication for theoretical physics is that, for extremal domains, the analytic content is a measure of non-commutativity of the (multiplicative) adjoint operators $T, T^{\dag}$, where $T^{\dag} = \bar z$, and therefore of the quantum deformation parameter (``Planck's constant"). The annular solution (which includes the disk as a special case) is, in fact, a continuous family of solutions, corresponding to all possible positive values of the deformation parameter, consistent with the physical requirement that conformal invariance in two dimensions forbids the existence of a special length scale.

Replacements for Mon, 13 May 24

[4]  arXiv:2204.11112 (replaced) [pdf, ps, other]

Title: Ultralimits, Amenable actions and Entropy

Authors: Elad Sayag

Comments: 50 pages. Changes include few typos removed, two sections moved into appendices and a section of "further problems" added

Subjects: Group Theory (math.GR)

[5]  arXiv:2403.16671 (replaced) [pdf, ps, other]

Title: Twisted conjugacy in dihedral Artin groups I: Torus Knot groups

Authors: Gemma Crowe

Comments: Comments welcome!

Subjects: Group Theory (math.GR); Computational Complexity (cs.CC)

[6]  arXiv:2404.04705 (replaced) [pdf, ps, other]

Title: Twisted conjugacy in dihedral Artin groups II: Baumslag Solitar groups $\mathrm{BS}(n,n)$

Authors: Gemma Crowe

Comments: Comments welcome!

Subjects: Group Theory (math.GR); Computational Complexity (cs.CC)

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