Simplicial volume, Barycenter method, and Bounded cohomology

Sungwoon Kim; Inkang Kim

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arXiv · 1503.02381

Simplicial volume, Barycenter method, and Bounded cohomology

Sungwoon Kim·Inkang Kim

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Abstract

We show that codimension one dimensional Jacobian of the barycentric straightening map is uniformly bounded for most of the higher rank symmetric spaces. As a consequence, we prove that the locally finite simplicial volume of most $\mathbb Q$-rank $1$ locally symmetric spaces is positive, which has been open for many years. Finally we improve the degree theorem for $\mathbb Q$-rank $1$ locally symmetric spaces of Connell and Farb. We also address the issue of surjectivity of the comparison map in real rank $2$ case.

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Sungwoon Kim, Inkang Kim. 2015-03-09. Simplicial volume, Barycenter method, and Bounded cohomology. https://arxiv.org/abs/1503.02381

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