Previously, we discussed that any big mapping class group is homeomorphic to the automorphism group of the curve graph.
We use this today to prove that any big mapping class group is neither locally compact nor compactly generated.
Further, we show that any big mapping class group is homeomorphic to the space of all irrational numbers.
Finally, we will discuss the pure mapping class group and its topological generating sets.
References:
Alexander method, Pure mapping class group, Dehn twist, Handle shift