Add to ORKGAbstract. We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in X. Inother words, orientable 4-manifolds are 2-systolically free. More generally, let m be a positive even integer, and let n>m. Then all manifolds of dimension at most n are m-systolically free (modulo torsion) if all k-skeleta, m +1 ≤ k ≤ n, of the loop space Ω(S m+1)arem-systolically free. 1
Gromov’s systolic estimate, first proved in [2], is considered one of the deepest results in systoli...
International audienceIn this article we explore the relationship between the systole and the diamet...
B. Shalen We give new information about the geometry of closed, orientable hyperbolic 3-manifolds wi...
Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifol...
Let X be a closed, orientable, smooth manifold of dimension 2m ≥ 6 with torsion-free middle-dimensio...
Abstract. If a closed smooth n-manifold M admits a finite cover M ̂ whose Z/2Z-cohomology has the ma...
A systolic inequality on a closed manifold M of dimension n is an inequality of the formDOLLARsys n ...
In 1949, C. Loewner proved in an unpublished work that the two-torus T satisfies an optimal systolic...
In 1949, C. Loewner proved in an unpublished work that the two-torus T satisfies an optimal systolic...
Abstract. We prove that closed manifolds of dimension 2m 6 with torsion-free middle-dimensional hom...
If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal...
This thesis is devoted to the study of universal geometric inequalities on Riemannian manifolds. Mor...
If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal...
Let X be a closed manifold of dimension 2m ≥ 6 with torsion-free middle-dimensional homology. We con...
Soit G un groupe de présentation finie. Un résultat de Gromov affirme l'existence de cycles géométri...
Gromov’s systolic estimate, first proved in [2], is considered one of the deepest results in systoli...
International audienceIn this article we explore the relationship between the systole and the diamet...
B. Shalen We give new information about the geometry of closed, orientable hyperbolic 3-manifolds wi...
Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifol...
Let X be a closed, orientable, smooth manifold of dimension 2m ≥ 6 with torsion-free middle-dimensio...
Abstract. If a closed smooth n-manifold M admits a finite cover M ̂ whose Z/2Z-cohomology has the ma...
A systolic inequality on a closed manifold M of dimension n is an inequality of the formDOLLARsys n ...
In 1949, C. Loewner proved in an unpublished work that the two-torus T satisfies an optimal systolic...
In 1949, C. Loewner proved in an unpublished work that the two-torus T satisfies an optimal systolic...
Abstract. We prove that closed manifolds of dimension 2m 6 with torsion-free middle-dimensional hom...
If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal...
This thesis is devoted to the study of universal geometric inequalities on Riemannian manifolds. Mor...
If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal...
Let X be a closed manifold of dimension 2m ≥ 6 with torsion-free middle-dimensional homology. We con...
Soit G un groupe de présentation finie. Un résultat de Gromov affirme l'existence de cycles géométri...
Gromov’s systolic estimate, first proved in [2], is considered one of the deepest results in systoli...
International audienceIn this article we explore the relationship between the systole and the diamet...
B. Shalen We give new information about the geometry of closed, orientable hyperbolic 3-manifolds wi...