Displaying 1101 – 1120 of 8745

Showing per page

Closed surfaces with different shapes that are indistinguishable by the SRNF

Eric Klassen, Peter W. Michor (2020)

Archivum Mathematicum

The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [5], provides a way of representing immersed surfaces in 3 , and equipping the set of these immersions with a “distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of 3 . Thus, it induces a distance function on the shape space of immersions, i.e., the space...

Cluster ensembles, quantization and the dilogarithm

Vladimir V. Fock, Alexander B. Goncharov (2009)

Annales scientifiques de l'École Normale Supérieure

A cluster ensemble is a pair ( 𝒳 , 𝒜 ) of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group Γ . The space 𝒜 is closely related to the spectrum of a cluster algebra [12]. The two spaces are related by a morphism p : 𝒜 𝒳 . The space 𝒜 is equipped with a closed 2 -form, possibly degenerate, and the space 𝒳 has a Poisson structure. The map p is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central role...

Currently displaying 1101 – 1120 of 8745