Two functions on $ \mathrm{Sp}(g,\mathbb{R})$

Patrick M. Gilmer

doi:10.1016/j.crma.2015.03.006

Homological algebra/Topology

Two functions on

Sp (g, R)

Presented by: Michèle Vergne

Patrick M. Gilmer ¹

¹ Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 477-481.

Abstract
Résumé

We consider two functions on $Sp (g, R)$ with values in the cyclic group of order four ${\pm 1, \pm i}$ . One was defined by Lion and Vergne. The other is −i raised to the power given by an integer valued function defined by Masbaum and the author (initially on the mapping class group of a surface). We identify these functions when restricted to $Sp (g, Z)$ . We conjecture the identity of these functions on $Sp (g, R)$ .

Nous considérons deux fonctions sur $Sp (g, R)$ à valeurs dans le groupe cyclique d'ordre quatre ${\pm 1, \pm i}$ . L'une a été définie par Lion et Vergne. L'autre est −i élevé à la puissance donnée par une fonction à valeurs entières définie par Masbaum et l'auteur (initialement sur le groupe modulaire d'une surface). Nous montrons que ces deux fonctions coïncident sur $Sp (g, Z)$ . Nous conjecturons qu'elles coïncident sur $Sp (g, R)$ .

Received: 2015-01-20
Accepted: 2015-03-19
Published online: 2015-04-04

DOI: 10.1016/j.crma.2015.03.006

Author's affiliations:

Patrick M. Gilmer ¹

¹ Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

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     title = {Two functions on $ \mathrm{Sp}(g,\mathbb{R})$},
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Patrick M. Gilmer. Two functions on $ \mathrm{Sp}(g,\mathbb{R})$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 477-481. doi : 10.1016/j.crma.2015.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.006/

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