Topological coarse shape groups
Zdravko Čuka, Nikola Koceiç Bilan · 2016
Coarse shape groups are well known algebraic invariants in (coarse) shape theory and homotopy theory, as well. Recently, topology was constructed on classical shape groups and it is proved that multiplication and taking inverses behave nice in respect of that topology, so we get topological shape groups. In this talk we will define topology on coarse shape groups, in some way a generalisation of previously mentioned topology, and we will prove that it also induces topological groups structure, which we naturally call topological coarse shape groups. They are topological-algebraic invariants of coarse shape theory and they have some good properties like completely regularity and independence of basepoints. It can be easily shown that we can consider topological shape groups as closed topological subgroups of topological coarse shape groups. Main result is that topological coarse shape groups can be obtained as the inverse limit of an inverse system of discrete topological groups. At the end we will discuss significance of these new structures.