q-Terms, singularities and the extended Bloch group

Understand

Our paper originated from a generalization of the Volume Conjecture to multisums of $q$-hypergeometric terms.

• This generalization was sketched by Kontsevich in a problem list in Aarhus University in 2006; \cite{Ko}.
• We introduce the notion of a $q$-hypergeometric term (in short, $q$-term).
• The latter is a product of ratios of $q$-factorials in linear forms in several variables.