On systolic zeta functions

Ivan Babenko (1) , Daniel Massart (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

We define Dirichlet type series associated with homology length spectra of Riemannian, or Finsler, manifolds, or polyhedra, and investigate some of their analytical properties. As a consequence we obtain an inequality analogous to Gromov's classical intersystolic inequality, but taking the whole homology length spectrum into account rather than just the systole.

Mots clés: systole; zeta function; stable norm; systole

Domaines: Géométrie différentielle [math.DG]

Ivan Babenko, Daniel Massart. On systolic zeta functions. European Journal of Mathematics, 2017, 3 (4), pp.899-915. ⟨10.1007/s40879-017-0181-1⟩. ⟨hal-01516391⟩