Kyed, DavidRaum, SvenVaes, StefaanValvekens, Matthias2017-10-092017-10-092017-10-09201710.2140/apde.2017.10.1757https://infoscience.epfl.ch/handle/20.500.14299/141115WOS:000409094100006We compute the L-2-Betti numbers of the free C*-tensor categories, which are the representation categories of the universal unitary quantum groups A(u)(F). We show that the L-2-Betti numbers of the dual of a compact quantum group G are equal to the L-2-Betti numbers of the representation category Rep. (G) and thus, in particular, invariant under monoidal equivalence. As an application, we obtain several new computations of L-2-Betti numbers for discrete quantum groups, including the quantum permutation groups and the free wreath product groups. Finally, we obtain upper bounds for the first L-2-Betti number in terms of a generating set of a C*-tensor category.L-2-Betti numbersrigid C*-tensor categoriesdiscrete quantum groupssubfactorscompact quantum groupstext::journal::journal article::research article