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Academic literature on the topic 'Géométrie systolique'
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Journal articles on the topic "Géométrie systolique"
Bulteau, Guillaume. "Géométrie systolique et technique de régularisation." Séminaire de théorie spectrale et géométrie 31 (2014): 1–41. http://dx.doi.org/10.5802/tsg.292.
Full textBalacheff, Florent. "Sur des problèmes de la géométrie systolique." Séminaire de théorie spectrale et géométrie 22 (2004): 71–82. http://dx.doi.org/10.5802/tsg.345.
Full textMir, Chady El, and Jacques Lafontaine. "Sur la géométrie systolique des variétés de Bieberbach." Geometriae Dedicata 136, no. 1 (June 25, 2008): 95–110. http://dx.doi.org/10.1007/s10711-008-9276-7.
Full textBabenko, Ivan K. "Géométrie systolique des variétés de groupe fondamental 𝐙 2." Séminaire de théorie spectrale et géométrie 22 (2004): 25–52. http://dx.doi.org/10.5802/tsg.342.
Full textBabenko, Ivan, and Florent Balacheff. "Géométrie systolique des sommes connexes et des revêtements cycliques." Mathematische Annalen 333, no. 1 (June 14, 2005): 157–80. http://dx.doi.org/10.1007/s00208-005-0668-9.
Full textEl Mir, Chady. "Géométrie systolique et métriques polyèdrales sur les 3-variétés de Bieberbach." Séminaire de théorie spectrale et géométrie 27 (2009): 101–15. http://dx.doi.org/10.5802/tsg.271.
Full textBavard, Christophe. "Une remarque sur la géométrie systolique de la bouteille de Klein." Archiv der Mathematik 87, no. 1 (July 2006): 72–74. http://dx.doi.org/10.1007/s00013-006-1665-2.
Full textDissertations / Theses on the topic "Géométrie systolique"
Yassine, Zeina. "Géométrie systolique extrémale sur les surfaces." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1074/document.
Full textIn 1949, C. Loewner proved in an unpublished work that the two-torus T satisfies an optimal systolic inequality relating the area of the torus to the square of its systole. By a systole here we mean the smallest length of a noncontractible loop in T. Furthermore, the equality is attained if and only if the torus is flat hexagonal. This result led to whatwas called later systolic geometry. In this thesis, we study several systolic-like inequalities. These inequalities involve the minimal length of various curves and not merely the systole.First we obtain three optimal conformal geometric inequalities on Riemannian Klein bottles relating the area to the product of the lengths of the shortest noncontractible loops in different free homotopy classes. We describe the extremal metrics in each conformal class.Then we prove optimal systolic inequalities on Finsler Mobius bands relating the systoleand the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimalsystolic inequality for Finsler Klein bottles with symmetries. We describe extremal metric families in both cases.Finally, we prove a critical systolic inequality on genus two surface. More precisely, it is known that the genus two surface admits a piecewise flat metric with conical singularities which is extremal for the systolic inequality among all nonpositively curved Riemannian metrics. We show that this piecewise flat metric is also critical for slow metric variations, this time without curvature restrictions, for another type of systolic inequality involving the lengths of the shortest noncontractible loops in different free homotopy classes. The free homotopy classes considered correspond to those of the systolic loops and the second-systolic loops of the extremal surface
Bulteau, Guillaume. "Sur des problèmes topologiques de la géométrie systolique." Thesis, Montpellier 2, 2012. http://www.theses.fr/2012MON20148/document.
Full textLet G be a finitely presented group. A theorem of Gromov asserts the existence of regular geometric cycles which represent a non null homology class h in the nth homology group with integral coefficients of G, geometric cycles which have a systolic volume as close as desired to the systolic volume of h. This theorem, of which no complete proof has been given, has lead to major results in systolic geometry. The first part of this thesis is devoted to a complete proof of this result.The regularizationtechnique consists in the use of these regular geometric cycles to obtain information about the class $h$. This technique allows to link the systolic volume of some closed manifolds to homotopical invariants of these manifolds, such as the minimal entropy and the Betti numbers. The second part of this thesis proposes to investigate these links.The third part of this thesis is devoted to three problems of systolic geometry. First we are investigating an inequality about embeded tori in $R^3$. Second, we are looking into minimal triangulations of compact surfaces and some information they can provide in systolic geometry. And finally, we are presenting the notion of simplicial complexity of a finitely-presented group and its links with the systolic geometry
Mir, Chady El. "Constante systolique des variétés de Bieberbach." Montpellier 2, 2009. http://www.theses.fr/2009MON20027.
Full textElmir, Chady. "Constante systolique et variétés plates." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2009. http://tel.archives-ouvertes.fr/tel-00439914.
Full textBalacheff, florent. "Inégalités isopérimétriques sur les graphes et applications en géométrie différentielle." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2005. http://tel.archives-ouvertes.fr/tel-00010580.
Full textMesmay, Arnaud de. "Topics in low-dimensional computational topology." Paris, École normale supérieure, 2014. https://theses.hal.science/tel-04462650v1.
Full textTopology is the area of mathematics investigating the qualitative properties of shapes and spaces. Although it has been a classical field of study for more than a century, it only appeared recently that being able to compute the topological features of various spaces might be of great value for many applications. This idea forms the core of the blossoming field of computational topology, to which this work belongs. The three contributions of this thesis deal with the development and the study of topological algorithms to compute deformations and decompositions of low-dimensional objects, such as graphs, surfaces or 3-manifolds. The first question we tackle concerns deformations: how can one test whether two graphs embedded on the same surface are isotopic, i. E. , whether one can be deformed continuously into the other? This kind of problems is relevant to practical problems arising with morphings or geographic information systems, for example. Relying on hyperbolic geometry and ideas from the theory of mapping class groups, we first establish a combinatorial criterion to characterize isotopy, reproving and strengthening a result of Ladegaillerie (1984). Combined with earlier algorithms on the homotopy of curves, this allows us in turn to provide efficient algorithms to solve this graph isotopy problem. We then shift our focus to decompositions, by investigating how to cut surfaces along curves or graphs with prescribed topological properties, which is an important routine in graph algorithms or computer graphics, amongst others domains. By establishing a strong connection with the continuous setting, as well as studying a discrete model for random surfaces, we improve the best known bounds for several instances of this problem. In particular, this proves a conjecture of Przytycka and Przytycki from 1993, and one of our new bounds readily translates into an algorithm to compute short pants decompositions. Finally, we move up one dimension, where the best known algorithms for many topological problems, like for example unknot recognition, are exponential. Most of these algorithms rely on normal surfaces, a ubiquitous tool to study the surfaces embedded in a 3-manifold. We investigate a relaxation of this notion called immersed normal surfaces, whose more convenient algebraic structure makes them good candidates to solve topological problems in polynomial time. We show that when working with immersed normal surfaces, a natural problem on the detection of singularities arises, and we prove it to be NP-hard – this is noteworthy as hardness results are very scarce in 3-dimensional topology. Our reduction works by establishing a connection with a restricted class of constraint satisfaction problems which has been partially classified by Feder