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Aristide Tsemo

Publications and source records attributed to Aristide Tsemo.

At least 19 recordsLinked to original sources
arXiv2022

Automorphisms of projective manifolds

Let $(M,P\nabla_M)$ be a compact projective manifold and $Aut(M,P\nabla_M)$ its group of automorphisms. The purpose of this paper is to study the topological properties of $(M,P\nabla_M)$ if $Aut(M,P\nabla_M))$ is not discrete by applying the results that I have shown in [13] and the Benzekri's functor which associates to a projective manifold a radiant affine manifold. This enables us to show that the orbits of the connected component of $Aut(M,P\nabla_M)$ are immersed projective submanifolds. We also classify $3$-dimensional compact projective manifolds such that $dim(Aut(M,P\nabla_M))\geq 2$.

math.DG↗
arXiv2016

Closed models, strongly connected components and Euler graphs

In this paper, we continue our study of closed models defined in categories of graphs. We construct a closed model defined in the cat-egory of directed graphs which characterizes the strongly connected components. This last notion has many applications, and it plays an important role in the web search algorithm of Brin and Page, the foun-dation of the search engine Google. We also show that for this closed model, Euler graphs are particular examples of cofibrant objects. This enables us to interpret in this setting the classical result of Euler which states that a directed graph is Euleurian if and only if the in degree and the out degree of every of its nodes are equal. We also provide a cohomological proof of this last result.

math.AT↗
arXiv2014

Cryptography and non commutative cohomology

In this paper, we study cryptography from a geometrical viewpoint. Let N be a network, we endow N with a natural Grothendieck topology. We use geometric representations of cohomological classes to define encryptions protocols. Link to link encryption is related to the notion of torsors. We use the notion of connective structure defined on a gerbe to define public encryption. We study statistical properties of data conveyed in a network, and define an entropy cocycle.

math.CT↗
arXiv2012

Some properties of schemes in group theory and Top couples

Let G be a group, and H a G-group defined by an imbedding map $G\rightarrow H$; in [12] we have defined a topology on a subset of normal subgroups of $H$, the so-called prime ideals. In this work, we generalize this topology to other classes of groups. We hope that such topologies define new effective tools to tackle well-known problems in groups theory. We study properties of the topology defined in [12], for example we define the notions of functor of points, dimension and outline a Galois theory.

math.AG↗
arXiv2011

Symbolic dynamics and the category of graphs

Symbolic dynamics is partly the study of walks in a directed graph. By a walk, here we mean a morphism to the graph from the Cayley graph of the monoid of non-negative integers. Sets of these walks are also important in other areas, such as stochastic processes, automata, combinatorial group theory, $C^*$-algebras, etc. We put a Quillen model structure on the category of directed graphs, for which the weak equivalences are those graph morphisms which induce bijections on the set of walks. We determine the resulting homotopy category. We also introduce a "finite-level" homotopy category which respects the natural topology on the set of walks. To each graph we associate a basal graph, well defined up to isomorphism. We show that the basal graph is a homotopy invariant for our model structure, and that it is a finer invariant than the zeta series of a finite graph. We also show that, for finite walkable graphs, if $B$ is basal and separated then the walk spaces for $X$ and $B$ are topologically conjugate if and only if $X$ and $B$ are homotopically equivalent for our model structure.

math.AT↗
arXiv2009

Gerbes for the Chow

Finding coherent relations to define non Abelian cohomology is a thriller which entertains the mathematical community since fifty one years. The purpose of this paper is to simplify the attempt to beat it defined by the author which used the notion of sequences of fibred categories and to apply the resulting theory to higher divisors and Chow theory.

math.CT↗
arXiv2009

Homotopy equivalence of isospectral graphs

In this paper, we investigate the Quillen model structure defined by Bisson and Tsemo in the category of directed graphs Gph. In particular, we give a precise description of the homotopy category of graphs associated to this model structure. We endow the categories of N-sets and Z-sets with related model structures, and show that their homotopy categories are Quillen equivalent to the homotopy category Ho(Gph). This enables us to show that Ho(Gph) is equivalent to the category cZSet of periodic Z-sets, and to show that two finite directed graphs are almost-isospectral if and only if they are homotopy-equivalent in our sense.

math.AT↗
arXiv2008

A homotopical algebra of graphs related to zeta series

The purpose of this paper is to develop a homotopical algebra for graphs, relevant to zeta series and spectra of finite graphs. More precisely, we define a Quillen model structure in a category of graphs (directed and possibly infinite, with loops and multiple arcs allowed). The weak equivalences for this model structure are the Acyclics (graph morphisms which preserve cycles). The cofibrations and fibrations for the model are determined from the class of Whiskerings (graph morphisms produced by grafting trees). Our model structure seems to fit well with the importance of acyclic directed graphs in many applications. In addition to the weak factorization systems which form this model structure, we also describe two Freyd-Kelly factorization systems based on Folding, Injecting, and Covering graph morphisms.

math.CO↗
arXiv2007

Extended powers and Steenrod operations in algebraic geometry

Steenrod operations have been defined by Voedvodsky in motivic cohomology in order to show the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper is to provide a setting for the construction of the Steenrod operations in algebraic geometry, for generalized cohomology theories whose formal group law has order two. We adapt the methods used by Bisson-Joyal in studying Steenrod and Dyer-Lashof operations in unoriented cobordism and mod 2 cohomology.

math.AG↗
arXiv2006

Deformation of homogeneous structures and homotopy of symplectomorphisms groups

Banyaga has shown that the group of symplectomorphisms Symp(N) of a compact symplectic manifold (N,w) determines the symplectic structure. This motivates the study of the homotopy properties of Symp(N). Gromov has shown that the group of symplectomorphisms of N is homotopic to SO(3)\times SO(3) when N is the product of two spheres endowed with the standard symplectic form. This result generalizes the study of the homotopy type of the group of diffeomorphisms of closed surfaces, by replacing the space of complex structures by pseudo-complex structures adapted to w. A complex structure on a surface induces on it a projective structure, the purpose of this paper is to study the action of Symp(N) on homogeneous structures defined on N, and to deduce homotopy properties of Symp(N).

math.DG↗
arXiv2005

Quadratic categories, Koszul resolutions and operads

A quadratic algebra is a homogeneous algebra generated by its elements of degree 1. Manin has endowed the category of quadratic algebras with two tensor products. These structures have been adapted to operads by Ginsburg and Kapranov. Berger has defined such tensor products for n-homogeneous algebras. The purpose of this paper is to define the notion of quadratic category, which is a category endowed with two tensor products. The Manin and Ginsburg-Kapranov constructions are examples of quadratic categories. We define also a Koszul complex, n-homogeneous operads and show how this notion can be applied to study coherence relations for n-categories.

math.CT↗
arXiv2003

Affine manifolds, lagrangian manifolds

Let $(M,ω)$ be a symplectic manifold endowed with a agrangian foliation ${\cal L}$, it has been shown by Weinstein [16] hat the symplectic structure of $M$ defines on each leaf of ${\cal L}$, connection which curvature and torsion forms vanish identically. uppose that $L_0$ is a compact leaf which Weinstein connection is eodesically complete, Molino and Curras-Bosch [2] have classified erms of such lagrangian foliation around $L_0$. In this paper we xtend this classification without supposing the completness of he compact leaf. The Weinstein connection is dual to the Bott onnection, this enables to relate the conjecture of Auslander nd Markus to transversally properties of these foliations.

math.DG↗
arXiv2003

Geometric structures on fields

Let M be a manifold, and G a Lie group which satisfies the unique extension property. An (M,G) manifold N is a manifold endowed with an atlas (U_i,f_i) where f_i is a diffeomorphism between U_i and an open set of M such that the coordinates change defined by this atlas are restriction of elements of G. We define the notion of geometric structures for toposes, and apply it to fields theory. We also interpret the Beyli theorem in this setting.

math.NT↗