Event Detail

Event Type: 
Topology Seminar
Monday, April 29, 2013 - 05:00
Gilkey 104

Speaker Info

Local Speaker: 

For group presentations with cyclic symmetry, there is a connection between asphericity of the (two-complex modeled on the) presentation and the dynamics of the cyclc shift automorphism for the group defined by the presentation. Specifically, if the presentation is "combinatorially aspherical" then the shift and its powers are fixed-point-free on the non-identity elements of the group. The converse holds for groups defined by cyclic presentations with positive relators of length three. Moreover, for these presentations the shift has a non-identity fixed point if and only if the group is finite.