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Symmetries of Maps on Surfaces
This is a brief overview of symmetry, its complexity and its applications of maps on surfaces. The details of this can be found in the references...
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A Note on Group Extensions and Proper 3-Realizability
The interaction between the study of three-dimensional manifolds and a particular stream of group theory has often been fruitful. In the realm of...
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Homology roses and the D(2)-problem
For a commutative ring R with a unit, an R -homology rose is a topological space whose homology groups with R -coefficients agree with those of a...
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CAT(0) spaces with polynomial divergence of geodesics
We construct a family of finite 2-complexes whose universal covers are CAT(0) and have polynomial divergence of desired degree. This answers a...
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Partitioning the triangles of the cross polytope into surfaces
We present a constructive proof that there exists a decomposition of the 2-skeleton of the k -dimensional cross polytope β k into closed surfaces of...
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Conformal Dimension And Random Groups
We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups.
We apply these bounds to the...
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Moves for standard skeleta of 3-manifolds with marked boundary
A 3-manifold with marked boundary is a pair ( M , X ), where M is a compact 3-manifold whose (possibly empty) boundary is made up of tori and Klein...
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Whitney’s formulas for curves on surfaces
The classical Whitney formula relates the number of times an oriented plane curve cuts itself to its rotation number and the index of a base point....
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Ellipses in translation surfaces
We study the topology and geometry of the moduli space of immersions of ellipses into a translation surface. The frontier of this space is naturally...
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Strong surjectivity of maps from 2-complexes into the 2-sphere
Given a model 2-complex K P of a group presentation P , we associate to it an integer matrix Δ P and we prove that a cellular map f : K ...
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Polyhedral Suspensions of Arbitrary Genus
A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fáry’s Theorem is established....
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Characterizing equivalent discrete Morse functions
We get a characterization theorem for equivalent discrete Morse functions defined on simplicial complexes in terms of their gradient vector field. As...
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On the boundary of a special class of hyperbolic two-dimensional simplicial complexes
A class of hyperbolic two-dimensional complexes X is defined. It is shown that the limit set of the action of π 1 ( X ) on the universal covering
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The p-Cockcroft Property of Central Extensions of Groups II
In [6], Çevik defined necessary and sufficient conditions for the presentation of a central extension of a cyclic group by an ordinary group to be p -C...
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Computing Matveev’s Complexity via Crystallization Theory: The Orientable Case
By means of a slight modification of the notion of GM-complexity introduced in [Casali, M.R., Topol. Its Appl. , 144 : 201–209, 2004], the present...
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Distortion of Surface Groups in CAT(0) free-by-cyclic Groups
Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to...
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On balanced presentations of the trivial group
To solve problems of Magnus and Stallings stated in the 1960s, we construct a balanced presentation of the trivial group such that no defining...