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gh-36128: Compute the characteristic varieties of a finitely presented group
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Let $G$ be a finitely presented group. For a field $\mathbb{k}$, let
$\Lambda:=\mathbb{k}[G]$ be its group algebra and let $\mathbb{T}$ be
its maximal spec, which is a torus. An element $\xi\in\mathbb{T}$
determines a local system of coefficients and the characteristic
varieties of $G$ are defined as
$$V_k(G):=\\{\xi\in\mathbb{T}\mid \dim H^1(G;\xi)\geq k\\}.$$
Except for the neutral element these are the reduced varieties of the
Fitting ideals of the Alexander matrix of the presentation. The function
`char_var` gives systems of generators of these ideals. A `groebner`
option is given to give Groebner basis; it is set as an option since the
computations may be quite long.
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URL: #36128
Reported by: Enrique Manuel Artal Bartolo
Reviewer(s): Enrique Manuel Artal Bartolo, miguelmarco, Travis Scrimshaw
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