Results 1 to 10 of about 25,976,263 (323)
Singularities of free group character varieties [PDF]
, 2009 Let Xr be the moduli space of SLn, SUn, GLn, or Un-valued representations of a rank r free group. We classify the algebraic singular stratification of Xr .
C. Florentino, Sean Lawton
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Homogeneity in the free group [PDF]
, 2010 We show that any non abelian free group $\F$ is strongly $\aleph_0$-homogeneous, i.e. that finite tuples of elements which satisfy the same first-order properties are in the same orbit under $\Aut(\F)$.
Chloé Perin, R. Sklinos
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A non-trivial example of a free-by-free group with the Haagerup property [PDF]
, 2012 The aim of this note is to prove that the group of Formanek-Procesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfies
François Gautero
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Group-Free 3D Object Detection via Transformers [PDF]
IEEE International Conference on Computer Vision, 2021 Recently, directly detecting 3D objects from 3D point clouds has received increasing attention. To extract object representation from an irregular point cloud, existing methods usually take a point grouping step to assign the points to an object ...
Ze Liu +4 more
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Homotopy type of the complex of free factors of a free group [PDF]
Proceedings of the London Mathematical Society, 2018 We show that the complex of free factors of a free group of rank n⩾2 is homotopy equivalent to a wedge of spheres of dimension n−2 . We also prove that for n⩾2 , the complement of (unreduced) Outer space in the free splitting complex is homotopy ...
Benjamin Brück, Radhika Gupta
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The Unipotency of Linear Groups Generated by Matrices with No More than Five Jorden Blocks
Journal of Harbin University of Science and Technology, 2022 Aiming at the question whether the group generated by two unipotent matrices whose Jordan blocks are of order no more than five is a unipotent group, based on the fundamental definition of nilpotent matrix, we use the matrix logarithm tool to obtain some
YANG Xin-song, LI Jia-xin
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The Number of Sides of a Parallelogram [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector ...
Elisha Falbel, Pierre-Vincent Koseleff
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Free groups defined by finite $p$-automata
Researches in Mathematics, 2023 For every odd prime $p$ we construct two $p$-automata with 14 inner states and prove that the group generated by 2 automaton permutations defined at their states is a free group of rank 2.
A.P. Krenevych, A.S. Oliynyk
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Measuring cones and other thick subsets in free groups [PDF]
International Journal of Group Theory, 2018 In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of ...
Elizaveta Frenkel +1 more
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The Unipotency of the Free Group with Linear Representation of Dimension 11
Journal of Harbin University of Science and Technology, 2022 For the unipotent problem of binary-generated free groups, the new trace equations are obtained by intensive study of combinatorial properties of the primitive element of the binary-generated free groups.
YANG Xin-song, XIA Xiao-dan
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