Abstract
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For any compact orientable irreducible
–manifold
with empty or incompressible toral boundary, the twisted
–torsion
is a nonnegative function defined on the representation variety
. We show that if
has infinite fundamental
group, then the
–torsion
function is strictly positive. Moreover, this torsion function is continuous when
restricted to the subvariety of upper triangular representations.
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Keywords
$3$–manifolds, twisted $L^2$–torsion
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Mathematical Subject Classification
Primary: 57K31
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Publication
Received: 27 October 2022
Revised: 3 January 2023
Accepted: 13 March 2023
Published: 16 July 2024
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