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Papers by Santiago López de Medrano
Scientiae Mathematicae japonicae, Mar 1, 2008
arXiv (Cornell University), Feb 1, 2020
In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of n... more In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of non-resonant characters from right-angled Artin groups onto the integer numbers, the module structure being with respect to the ring K[t ±1 ], where K is a field of characteristic zero. Papadima and Suciu determined some part of this structure by means of the flag complex of the graph of the Artin group. In this work, we provide more properties of the torsion part of this module, e.g., the dimension of each primary part and the maximal size of Jordan forms (if we interpret the torsion structure in terms of a linear map). These properties are stated in terms of homology properties of suitable filtrations of the flag complex and suitable double covers of an associated toric complex.
Biological Rhythm Research, Feb 1, 2005
Abstract We present some conclusions of our experience as a group of biologists and mathematician... more Abstract We present some conclusions of our experience as a group of biologists and mathematicians in modeling circadian rhythms. These conclusions involve a reflection on the general interrelations between Biology and Mathematics and between experiments, models and theories. We ...
Lecture Notes in Mathematics, 1988
Without Abstract
Lecture Notes in Mathematics, 1989
Without Abstract
Springer eBooks, 2008
The importance of both ultradian and circadian rhythms in Nature is well known. In the literature... more The importance of both ultradian and circadian rhythms in Nature is well known. In the literature it is possible to find many articles referring to the characteristics and properties of such rhythms and, in some cases, of their mathematical modeling. However, as far as we know, there is not enough information relating these two types of rhythms either from a
Bulletin of the American Mathematical Society, Sep 1, 1967
Boletim da Sociedade Brasileira de Matemática, Sep 1, 1997
In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear... more In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear complex dynamical systems. For every integer n > 3, and an ordered partition of n into an odd number k of positive integers we construct such a manifold together with an (n-2)-dimensional space of complex structures. We show that, under mild additional hypotheses, these deformation spaces are universal. Some of these manifolds are holomorphically equivalent to some known examples and we stablish the identification with them. But we also obtain new manifolds admitting a complex structure, and we describe the differentiable type of some of them.
CRC Press eBooks, Mar 3, 2003
Lecture Notes in Mathematics, 1972
Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such ... more Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such a pair corresponds with a smooth action of Z on N, where the action of a generator is given by f. The study and the classification of such pairs, even for a given ...
Contemporary mathematics, 2001
We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Cateno... more We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid that avoids some problems present in the original depiction of these surfaces.
Contemporary mathematics, 2008
Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis H... more Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis Hernandez de la Cruz and Santiago Lopez de Medrano Dedicated to Le Dung Trang on his 60th birthday. ABSTRACT. We ...
Trends in mathematics, 2017
Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ... more Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ∈ R k. It is well known that the condition for Z to be a smooth variety (known as weak hyperbolicity) is that the origin in R k is not a convex combination of any collection of k of the vectors Ai. We interpret this condition as a transversality property in order to approach the case when it is singular and we extend some results known for the smooth case, in particular the computation of the homology groups of Z in terms of the combinatorics of the natural quotient polytope. We show that Z cannot be an exotic homotopy sphere nor a non-simply connected homology sphere and use this to show that, except for some clearly characterized degenerate cases, when Z is not smooth it cannot be a topological or even a homological manifold.
Comptes Rendus Mathematique, Jun 1, 2005
Under fairly general hypotheses, we investigate by elementary methods the structure of the p-peri... more Under fairly general hypotheses, we investigate by elementary methods the structure of the p-periodic orbits of a family h u of transformations near (u 0 , x 0) when h u 0 (x 0) = x 0 and dh u 0 (x 0) has a simple eigenvalue which is a primitive p-th root of unity. To cite this article: M.
Comptes Rendus Mathematique, Oct 1, 2008
All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in... more All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in generalized Hopf bifurcations. To cite this article: M.
Scientiae Mathematicae japonicae, Mar 1, 2008
arXiv (Cornell University), Feb 1, 2020
In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of n... more In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of non-resonant characters from right-angled Artin groups onto the integer numbers, the module structure being with respect to the ring K[t ±1 ], where K is a field of characteristic zero. Papadima and Suciu determined some part of this structure by means of the flag complex of the graph of the Artin group. In this work, we provide more properties of the torsion part of this module, e.g., the dimension of each primary part and the maximal size of Jordan forms (if we interpret the torsion structure in terms of a linear map). These properties are stated in terms of homology properties of suitable filtrations of the flag complex and suitable double covers of an associated toric complex.
Biological Rhythm Research, Feb 1, 2005
Abstract We present some conclusions of our experience as a group of biologists and mathematician... more Abstract We present some conclusions of our experience as a group of biologists and mathematicians in modeling circadian rhythms. These conclusions involve a reflection on the general interrelations between Biology and Mathematics and between experiments, models and theories. We ...
Lecture Notes in Mathematics, 1988
Without Abstract
Lecture Notes in Mathematics, 1989
Without Abstract
Springer eBooks, 2008
The importance of both ultradian and circadian rhythms in Nature is well known. In the literature... more The importance of both ultradian and circadian rhythms in Nature is well known. In the literature it is possible to find many articles referring to the characteristics and properties of such rhythms and, in some cases, of their mathematical modeling. However, as far as we know, there is not enough information relating these two types of rhythms either from a
Bulletin of the American Mathematical Society, Sep 1, 1967
Boletim da Sociedade Brasileira de Matemática, Sep 1, 1997
In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear... more In this paper we study a family of complex, compact, non-symplectic manifolds arising from linear complex dynamical systems. For every integer n > 3, and an ordered partition of n into an odd number k of positive integers we construct such a manifold together with an (n-2)-dimensional space of complex structures. We show that, under mild additional hypotheses, these deformation spaces are universal. Some of these manifolds are holomorphically equivalent to some known examples and we stablish the identification with them. But we also obtain new manifolds admitting a complex structure, and we describe the differentiable type of some of them.
CRC Press eBooks, Mar 3, 2003
Lecture Notes in Mathematics, 1972
Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such ... more Consider pairs (M,f), where M is a compact smooth manifold and f:M--*M is a diffeomorphism. Such a pair corresponds with a smooth action of Z on N, where the action of a generator is given by f. The study and the classification of such pairs, even for a given ...
Contemporary mathematics, 2001
We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Cateno... more We give a parameterization, using Jacobi's elliptic functions, of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid that avoids some problems present in the original depiction of these surfaces.
Contemporary mathematics, 2008
Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis H... more Page 93. Contemporary Mathematics Volume 475, 2008 Some Families of Isolated Singularities Luis Hernandez de la Cruz and Santiago Lopez de Medrano Dedicated to Le Dung Trang on his 60th birthday. ABSTRACT. We ...
Trends in mathematics, 2017
Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ... more Let Z ⊂ R n be given by k + 1 equations of the form n i=1 Aix 2 i = 0, n i=1 x 2 i = 1, where Ai ∈ R k. It is well known that the condition for Z to be a smooth variety (known as weak hyperbolicity) is that the origin in R k is not a convex combination of any collection of k of the vectors Ai. We interpret this condition as a transversality property in order to approach the case when it is singular and we extend some results known for the smooth case, in particular the computation of the homology groups of Z in terms of the combinatorics of the natural quotient polytope. We show that Z cannot be an exotic homotopy sphere nor a non-simply connected homology sphere and use this to show that, except for some clearly characterized degenerate cases, when Z is not smooth it cannot be a topological or even a homological manifold.
Comptes Rendus Mathematique, Jun 1, 2005
Under fairly general hypotheses, we investigate by elementary methods the structure of the p-peri... more Under fairly general hypotheses, we investigate by elementary methods the structure of the p-periodic orbits of a family h u of transformations near (u 0 , x 0) when h u 0 (x 0) = x 0 and dh u 0 (x 0) has a simple eigenvalue which is a primitive p-th root of unity. To cite this article: M.
Comptes Rendus Mathematique, Oct 1, 2008
All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in... more All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in generalized Hopf bifurcations. To cite this article: M.