 Endomorphisms of Artin groups of type Ã_{n}. (with L. Paris, submitted)
[ pdf ▪
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We determine a classification of the endomorphisms of the Artin group of affine type Ã_{n} for n≥4.
 Divergence, thickness and hypergraph index for general Coxeter groups. (with P. Dani,
Y. Naqvi and A. Thomas,
accepted in Israel Journal of Mathematics)
[ pdf ▪
arxiv ▪
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abstract ]
We introduce a computable combinatorial invariant, hypergraph index, for arbitrary Coxeter systems, which generalizes
the construction of Levcovitz for rightangled Coxeter groups. We use it to obtain an upper bound on the order of divergence
of general Coxeter groups. This upper bound is sharp for some infinite families of nonrightangled Coxeter groups,
and conjecturally, for all Coxeter groups.
 Property R_{∞} for some spherical and affine ArtinTits groups.
(with M. Calvez)
Journal of Group Theory 25, 6 (2022), 10451054
[ pdf ▪
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abstract ]
We give a short uniform proof of property R_{∞}
for the ArtinTits groups of spherical types A_{n}, B_{n}, D_{4}, I_{2}(m),
their pure subgroups, and for the ArtinTits groups of affine types Ã_{n1} and C̃_{n}
for n≥2.

Homological Dehn functions of groups of type FP_{2}.
(with N. Brady and R. Kropholler, submitted)
[ pdf ▪
arXiv ▪
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abstract ]
We study the properties of homological Dehn functions of groups of type FP_{2}. We show how to build uncountably many quasiisometry classes of such groups with a given homological Dehn function. As an application we prove that there exists a group of type FP_{2} with quartic homological Dehn function and unsolvable word problem.

Artin groups of types F_{4} and H_{4} are not commensurable with that of type D_{4}.
Topology and its Applications 300 (2021), 107770
[ pdf ▪
arXiv ▪
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We resolve two out of six cases left undecided in a recent article of Cumplido and Paris. We also determine the automorphism group of Art(D_{4}) and describe torsion elements, their orders and conjugacy classes in all Artin groups of spherical type modulo their centers.

Linearity of some lowcomplexity mapping class groups. Forum Mathematicum 32 (2020), no. 2, 279286
[ pdf ▪
arXiv ▪
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zbMATH ▪
abstract ]
We show that the pure mapping class group of the orientable surface of genus g with b boundary components and n punctures is linear for the following values of (g,b,n): (0,m,n), (1,2,0), (1,1,1), (1,0,2), (1,3,0), (1,2,1), (1,1,2), (1,0,3).
A (longer) earlier version with an alternative computation "from first principles": [ pdf ]

Realizable ranks of joins and intersections of subgroups in free groups.
International Journal of Algebra and Computation
30 (2020), no. 3, 625666
[ pdf ▪
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We describe the locus of possible ranks ( rk(H∨K), rk(H∩K) ) for any given subgroups H, K of a free group. In particular, we resolve the remaining open case (m=4) of R.Guzman's "GroupTheoretic Conjecture" in the affirmative.

Uncountably many quasiisometry classes of groups of type FP.
(with R. Kropholler and
I. Leary)
American Journal of
Mathematics 142, 6 (2020), 19311944
[ pdf ▪
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We prove that among I. Leary's groups of type FP there exist uncountably many nonquasiisometric ones. We also prove that for each n≥4 there exist uncountably many quasiisometry classes of nonfinitely presented ndimensional Poincare duality groups.

Genus bounds in rightangled Artin groups.
(with M. Forester and J. Tao)
Publicacions Matemàtiques 64 (2020), no. 1, 233253
[ pdf ▪
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abstract ]
We generalize Culler's proof for the lower bound for the stable commutator length in free groups to the case of rightangled Artin groups.

Dehn functions of subgroups of rightangled Artin groups. (with N. Brady)
Geometriae Dedicata 200 (2019), 197239
[ pdf ▪
arXiv (old version) ▪
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MathReviews ▪
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abstract ]
We show that polynomials of arbitrary integer degree are realizable as Dehn functions of subgroups in rightangled Artin groups. In the Appendix we prove that no finite index subgroup of the famous Gersten's freebycyclic group can be embedded into a rightangled Artin group.
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