Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra

R. Grigorchuk, P. H. Leemann, T. Nagnibeda

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear (p.l.) spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given set of p.l. spaces we define and discuss (normalized) Einstein flows. p.l. Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated.

Original languageEnglish
Article number205004
JournalJournal of Physics A: Mathematical and Theoretical
Issue number20
Publication statusPublished - 18 Apr 2016
Externally publishedYes


  • Lattice gravity
  • PDE methods
  • Regge calculus
  • equations of motion
  • methods of Riemannian geometry


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