TL;DR
This paper investigates two functions on the symplectic group Sp(g,R) with values in the cyclic group of order four, identifying their relationship on Sp(g,Z) and conjecturing their equivalence on the entire group.
Contribution
The paper explicitly identifies two previously defined functions on Sp(g,Z) and conjectures their equality on the larger group Sp(g,R).
Findings
Functions are identical on Sp(g,Z).
Conjecture: functions are equal on Sp(g,R).
Provides a link between functions defined by Lion-Vergne and Masbaum-Author.
Abstract
We consider two functions on Sp(g,R) with values in the cyclic group of order four {1,-1,i,-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).
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