Higher-order preconnections in synthetic differential geometry of jet bundles.
Infinitesimal and local structures for Banach spaces and its exponentials in a topos
Logical opens of exponential objects
Metric Ricci Curvature and Flow for PL Manifolds
We summarize here the main ideas and results of our papers [28], [14], as presented at the 2013 CIRM Meeting on Discrete curvature and we augment these by bringing up an application of one of our main results, namely to solving a problem regarding cube complexes.
Models for synthetic integration theory.
Models for synthetic supergeometry
O čtvrtém Hilbertově problému
O množině středů křivek konstantní křivosti rozšířené hyperbolické roviny, které procházejí daným bodem hyperbolické roviny a dotýkají se dané křivky konstantní křivosti
On analytic models of synthetic differential geometry
On the integration theorem for Lie groupoids
Ordinary differential equations and their exponentials
In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.
Principal bundles, groupoids, and connections
We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.
Réseaux de Coxeter-Davis et commensurateurs
For each integer and each finite graph , we construct a Coxeter group and a non positively curved polygonal complex on which acts properly cocompactly, such that each polygon of has edges, and the link of each vertex of is isomorphic to . If is a “generalized -gon”, then is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on for to be non enumerable (which is satisfied if is a thick classical generalized -gon). On the other hand,...
Some cases of compatibility of the tangency relations of sets.
Strong infinitesimal linearity, with applications to strong difference and affine connections
Sur les modèles de la géométrie différentielle synthétique
Synthetic differential geometry of higher-order total differentials
Synthetic Reasoning In Differential Geometry.
The affine bundle theorem in synthetic differential geometry of jet bundles.
The Tangent cone of an Aleksandrov space of curvature.