For instance , the surjectivity part implies the Kadison -- Kaplansky conjecture for a discrete torsion - free group , and the injectivity is closely related to the Novikov conjecture .
The conjecture , if true , would have some older famous conjectures as consequences .
The surjectivity part implies the Kadison -- Kaplansky conjecture for a discrete torsion - free group , and the injectivity is closely related to the Novikov conjecture .
The conjecture , if true , would have some older famous conjectures as consequences .