| Kommentar |
We will discuss a recent work of Christian Rosendal on coarse geometry of topological
groups. We will explore concepts such as the word metric, quasi-isometry, coarse
embedding for Polish groups. Typical examples of groups we will be interested in
are isometry groups of separable metric spaces, automorphism groups of countable
structures, Banach spaces with the addition operation or homeomorphism groups of
compact separable spaces. The seminar will be of interest to students in model theory,
geometric group theory, and functional analysis. The main reference will be the book
manuscript [3]. |
| Literatur |
[1] S. Gao, Invariant Descriptive Set Theory, Pure and applied mathematics.
Chapman & HallCRC, Boca Raton, 2009, xiv + 392 pp.
[2] K. Mann, C. Rosendal, Large-scale geometry of homeomorphism groups,
Ergodic Theory Dynam. Systems 38 (2018), no. 7, 2748-2779.
[3] C. Rosendal, Coarse Geometry of Topological Groups, (book manuscript,
version of March 2018),
http://homepages.math.uic.edu/~rosendal/PapersWebsite/Coarse-Geometry-Book17.pdf
[4] C. Rosendal, Equivariant geometry of Banach spaces and topological
groups, Forum of Mathematics, Sigma, (2017), Vol. 5, e22, 62 pages.
[5] C. Rosendal, Large scale geometry of automorphism groups,
arXiv:1403.3107
[6] C. Rosendal, Large scale geometry of metrisable groups, arXiv: 1403.3106.
[7] C. Rosendal, Global and local boundedness of Polish groups, Indiana
Univ. Math. J. 62 (2013), no. 5, 1621-1678.
[8] C. Rosendal, A topological version of the Bergman property, Forum
Mathematicum 21 (2009), no. 2, 299-332.
[9] J. Zielinski, Locally Roelcke precompact groups, arXiv:1806.03752.
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eG