Secondary invariants associated to positive scalar curvature metrics on closed spin manifolds have been used to study the space of such metrics on a fixed manifold. I will first talk about a result of Piazza-Schick which uses torsion in the fundamental group to prove the existence of infinitely many bordism classes of psc metrics on certain closed manfiolds. In particular, the space of psc metrics on such manifolds has infinitely many connected components. Then, I will report on some ongoing work with Simone Cecchini and Vito Felice Zenobi, where we define a relative verison of the Cheeger-Gromov rho-invariant for manifolds with boundary with the aim of proving analogues of the results of Piazza-Schick for such manifolds.
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