On Thompson's group T and algebraic K-theory

Abstract

Using a theorem of Lück-Reich-Rognes-Varisco, we show that the Whitehead group of Thompson's group T is infinitely generated, even when tensored with the rationals. To this end we describe the structure of the centralizers and normalizers of the finite cyclic subgroups of T, via a direct geometric approach based on rotation numbers. This also leads to an explicit computation of the source of the Farrell-Jones assembly map for the rationalized higher algebraic K-theory of the integral group ring of T.

Final version, 12 pages

References in corpus (4)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Algebraic K-theory of group rings and the cyclotomic trace map
• Algorithms and Classification in Groups of Piecewise-Linear Homeomorphisms
• K- and L-theory of group rings

Cited by in corpus (4)

• Algebraic K-theory of group rings and the cyclotomic trace map
• Algebraic $K$-theory, assembly maps, controlled algebra, and trace methods
• Cohomological finiteness conditions and centralisers in generalisations of Thompson's group V
• Towards computing the rational homology and assembly maps of generalised Thompson groups