On the Hodge spectra of lens spaces

OpenYear of origin: 2021

Posted online: 2022-01-25 05:15:32Z by SciLag Admin21

Cite as: P-220125.1

  • Differential Geometry
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Problem's Description

In [1], R. Miatello suggests the following problems:

1) Construct congruence lattices which are norm$_1$ and norm$_1*$- isospectral in all dimensions (see [2]).

2) Are there families of $p$-isospectral lens spaces for all $p$, with more than two elements?

3) Give a procedure to go from $p$-isospectral lens spaces (for all $p$) of dimension $m$ to dimension $m + 1$.

4) Establish connections with toric geometry (see [3]).

  1. ArticleIs an originA list of open problems in differential geometry

    São Paulo Journal of Mathematical Sciences 15, 305-321, 2021fulltext

  2. Article Spectra of lens spaces from 1-norm spectra of congruence lattices

    International Mathematics Research Notices. IMRN, 1054-1089, 2016fulltext

  3. Article On a relation between spectral theory of lens spaces and Ehrhart theory

    Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae. New Series 28, 556-565, 2017fulltext

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  • Created at: 2022-01-25 05:15:32Z