INVESTIGADORES
LAURET Emilio Agustin
artículos
Título:
Spectra of lens spaces from 1-norm spectra of congruence lattices
Autor/es:
EMILIO AGUSTÍN LAURET; MIATELLO, ROBERTO JORGE; ROSSETTI, JUAN PABLO
Revista:
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Editorial:
OXFORD UNIV PRESS
Referencias:
Lugar: Oxford; Año: 2016 vol. 2016 p. 1054 - 1089
ISSN:
1073-7928
Resumen:
To every $n$-dimensional lens space $L$, we associate a congruence lattice $mathcal L$ in $Z^m$, with $n=2m-1$ and we prove a formula relating the multiplicities of Hodge-Laplace eigenvalues on $L$ with the number of lattice elements of a given $ orma{cdot}$-length in $mathcal L$. As a consequence, we show that two lens spaces are isospectral on functions (resp. isospectral on $p$-forms for every $p$) if and only if the associated congruence lattices are $ orma{cdot}$-isospectral (resp. $ orma{cdot}$-isospectral plus a geometric condition). Using this fact, we give, for every dimension $nge 5$, infinitely many examples of Riemannian manifolds that are isospectral on every level $p$ and are not strongly isospectral.