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Markoff-Rosenberger triples in arithmetic progression
(Elsevier, 2013-06)
We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in ...
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Smash products for secondary homotopy groups
(Springer, 2008-10)
We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered.
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The stability of the Kronecker products of Schur functions
(Elsevier, 2011-04-01)
In the late 1930’s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, the values of the Kronecker coefficients appearing in the product ...
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Equimultiple locus of embedded algebroid surfaces and blowing-up in characteristic zero
(Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 2004)
The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution process, both classical and modern.In this paper we explore how it changes by blowing–up.
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Logarithmic cohomology of the complement of a plane curve
(Springer, 2002-03)
Let D, x be a plane curve germ. We prove that the complex Ω•(log D)x computes the cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial converse to a theorem of F.J. Castro-Jiménez, D. Mond ...
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Extreme Khovanov spectra
(EUROPEAN MATHEMATICAL SOC, 2019-09-28)
We prove that the spectrum constructed by González-Meneses, Manchón and the second author is stably homotopy equivalent to the Khovanov spectrum of Lipshitz and Sarkar at its extreme quantum grading.
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A fast solution to the conjugacy problem in the four-strand braid group
(De Gruyter, 2014-09)
We present an algorithm for solving the conjugacy search problem in the fourstrand braid group. The computational complexity is cubic with respect to the braid length.
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Geometric embeddings of braid groups do not merge conjugacy classes
(Sociedad Matemática Mexicana, 2014-10)
An embedding of the m-times punctured disc into the n-times punctured disc, for n > m, yields an embedding of the braid group on m strands Bm into the braid group on n strands Bn, called a geometric embedding. The main ...
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On loxodromic actions of Artin–Tits groups
(Elsevier, 2018-04-10)
Artin–Tits groups act on a certain delta-hyperbolic complex, called the “additional length complex”. For an element of the group, acting loxodromically on this complex is a property analogous to the property of being ...
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Hodge ideals of free divisors
(Springer, 2022-04-18)
We consider the Hodge filtration on the sheaf of meromorphic functions along free divisors for which the logarithmic comparison theorem holds. We describe the Hodge filtration steps as submodules of the order filtration ...