We show that mapping tori of polynomially-growing automorphisms of many non-positively curved groups have vanishing homology torsion growth. In the case of free-by-cyclic groups with polynomially-growing monodromy, this confirms a conjecture of Lück relating the integral torsion and the $L^2$-torsion of a group. Our main tool is the cheap rebuilding property introduced by Abert—Bergeron—Fraczyk—Gaboriau. This is based on joint work with Naomi Andrew, Yassine Guerch and Sam Hughes.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/HOGRO2024