Coarse geometry of pure mapping class groups of infinite graphs. (English) Zbl 1522.20168
The authors study mapping class groups of locally finite infinite graphs. The pure mapping class group is the subgroup of the mapping class group where the ends are fixed pointwise.
The cases when the pure mapping class group of a locally finite, infinite graph is globally coarsely bounded and when it is locally coarsely bounded are classified.
They also establish lower bounds on the first integral cohomology of the pure mapping class group for some graphs and compute the asymptotic dimension of all locally coarsely bounded pure mapping class groups of infinite rank graphs.
The cases when the pure mapping class group of a locally finite, infinite graph is globally coarsely bounded and when it is locally coarsely bounded are classified.
They also establish lower bounds on the first integral cohomology of the pure mapping class group for some graphs and compute the asymptotic dimension of all locally coarsely bounded pure mapping class groups of infinite rank graphs.
Reviewer: Stephan Rosebrock (Karlsruhe)
MSC:
| 20F65 | Geometric group theory |
| 05C63 | Infinite graphs |
| 57K20 | 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) |
| 57M15 | Relations of low-dimensional topology with graph theory |
| 05C10 | Planar graphs; geometric and topological aspects of graph theory |
| 20E36 | Automorphisms of infinite groups |
| 20F38 | Other groups related to topology or analysis |
Keywords:
mapping class groups; \( \operatorname{Out}( F_n)\); proper homotopy equivalence; coarse geometry; Polish groups; asymptotic dimensionReferences:
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