LAURET Emilio Agustin
congresos y reuniones científicas
Lens spaces isospectral on p-forms for every p
LAURET, EMILIO A.
Congreso; International Conference of Mathematicians 2014; 2014
International Mathematical Union
To every lens space $L$ we associate a congruence lattice $mathcal L$ in $mathbb Z^m$, showing that two lens spaces $L$ and $L´$ are isospectral on functions if and only if the associated lattices $mathcal L$ and $mathcal L´$ are isospectral with respect to one-norm. We also prove that $L$ and $L´$ are isospectral on $p$-forms for every $p$ if and only if $L$ and $L´$ are one-norm isospectral and satisfy a stronger condition. By constructing such congruence lattices we give infinitely many pairs of 5-dimensional lens spaces that are $p$-isospectral for all $p$. Such pairs are the first example of compact connected Riemannian manifolds $p$-isospectral for all $p$ but not strongly isospectral; in particular, they cannot be constructed by Sunada´s method.