Locally Compact Topologies on Piecewise Full Groups of Cantor Homeomorphisms
A criterion for when a piecewise (topological) full group of homeomorphisms of the Cantor space carries a non-discrete totally disconnected locally compact topology, and for when the associated alternating full group is compactly generated. Applying it yields a systematic family of t.d.l.c. groups whose derived group is non-discrete, compactly generated, open and simple, unifying the earlier Neretin, Rover and Lederle constructions and revealing the universal role of alternating full groups in the local structure theory of simple t.d.l.c. groups.
LOCALLY COMPACT PIECEWISE FULL GROUPS OF HOMEOMORPHISMS ALEJANDRA GARRIDO AND COLIN D. REID
A group-theory study of when a piecewise (topological) full group of homeomorphisms of the Cantor space admits a non-discrete totally disconnected locally compact (t.d.l.c.) group topology, together …