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Stable integral simplicial volume of 3-manifolds

Stable integral simplicial volume of 3-manifolds
Date:

12.12.2019

Place:

2.058 (20.30)

Speaker:

Marco Moraschini

Time:

15:45

Abstract: Simplicial volume is a homotopy invariant of compact manifolds introduced by Gromov in his pioneering paper "Volume and bounded cohomology" (1982). Roughly speaking, it measures the complexity of a manifold in terms of its singular chains with real coefficients. A celebrated conjecture of Gromov claims that the Euler characteristic of an oriented closed aspherical manifold with vanishing simplicial volume is zero.
A possible strategy for proving the previous conjecture is to work with a variation of the ordinary simplicial volume called stable integral simplicial volume. Indeed, the vanishing of the stable integral simplicial volume implies the vanishing of the Euler characteristic. For this reason, a classical question is to determine which manifolds admit an integral approximation (i.e. manifolds such that the simplicial volume agrees with the stable integral simplicial volume). In this talk, we prove show that most of prime 3-manifolds admit an integral approximation.
This is a joint work with Daniel Fauser, Clara Löh and José Pedro Quintanilha.