Journal of the Mathematical Society of Japan

Rank two jump loci for solvmanifolds and Lie algebras

Ştefan PAPADIMA and Laurenţiu PAUNESCU

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Abstract

We consider representation varieties in $SL_2$ for lattices in solvable Lie groups, and representation varieties in $\mathfrak{sl}_2$ for finite-dimensional Lie algebras. Inside them, we examine depth 1 characteristic varieties for solvmanifolds, respectively resonance varieties for cochain Differential Graded Algebras of Lie algebras. We prove a general result that leads, in both cases, to the complete description of the analytic germs at the origin, for the corresponding embedded rank 2 jump loci.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 2 (2018), 695-709.

Dates
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1524038670

Digital Object Identifier
doi:10.2969/jmsj/07027438

Mathematical Reviews number (MathSciNet)
MR3787736

Zentralblatt MATH identifier
06902438

Subjects
Primary: 55N25: Homology with local coefficients, equivariant cohomology
Secondary: 17B56: Cohomology of Lie (super)algebras 20J06: Cohomology of groups 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

Keywords
representation variety characteristic variety resonance variety analytic germ solvmanifold Lie algebra

Citation

PAPADIMA, Ştefan; PAUNESCU, Laurenţiu. Rank two jump loci for solvmanifolds and Lie algebras. J. Math. Soc. Japan 70 (2018), no. 2, 695--709. doi:10.2969/jmsj/07027438. https://projecteuclid.org/euclid.jmsj/1524038670


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