Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Vector-relation configurations and plabic graphs

Abstract : We study a simple geometric model for local transformations of bipartite graphs. The state consists of a choice of a vector at each white vertex made in such a way that the vectors neighboring each black vertex satisfy a linear relation. Evolution for different choices of the graph coincides with many notable dynamical systems including the pentagram map, Q-nets, and discrete Darboux maps. On the other hand, for plabic graphs we prove unique extendability of a configuration from the boundary to the interior, an elegant illustration of the fact that Postnikov's boundary measurement map is invertible. In all cases there is a cluster algebra operating in the background, resolving the open question for Q-nets of whether such a structure exists.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02595570
Contributor : Sanjay Ramassamy <>
Submitted on : Friday, May 15, 2020 - 8:09:26 PM
Last modification on : Wednesday, April 14, 2021 - 12:13:01 PM

File

Vectors and relations on bipar...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02595570, version 1

Citation

Niklas Affolter, Max Glick, Pavlo Pylyavskyy, Sanjay Ramassamy. Vector-relation configurations and plabic graphs. 2020. ⟨hal-02595570⟩

Share

Metrics

Record views

29

Files downloads

19