Adam Clay

Similar to how the integers can be equipped with an ordering that is invariant with respect to addition, many groups can be equipped with an ordering that is invariant under the group operation. But aside from being a curious generalization of a...

The Cascade Topology Seminar is supported in part by grants from the National Science Foundation, the Pacific Institute for the Mathematical Sciences, and is a Mathematical Sciences Research Institute MER Network Conference. The support of these...

There is a growing body of work that supports a connection between L-spaces and 3-manifolds with non-left-orderable fundamental group, in fact a Seifert fibred manifold is an L-space if and only if its fundamental group is not left-orderable. In this...

A group is left-orderable if it has a strict total ordering that is invariant under multiplication from the left. For countable groups, this is equivalent to acting on the real line by order-preserving homeomorphisms. A group being circularly...

When a group acts faithfully by orientation-preserving homeomorphisms on S^1, one can sometimes use the action on S^1 to prove the existence of a faithful order-preserving action by homeomorphisms on the real line. This can be reworded in algebraic...