Cohomological Waves

Thursday, November 21, 2013 - 1:30pm - 2:30pm
Lind 305
Yiqing Cai (University of Minnesota, Twin Cities)
Waves are usually treated analytically. Another viewpoint to exam periodic waves is topologically, by looking at the map from the space which the waves lie on, to the period, which we think as a circle. Especially, if the space has non-trivial first homology, the degree (or winding number) of the map gives some information about the waves. One could extend the idea of degree to discrete time periodic waves, which has many applications in coverage problems in sensor networks. The results show that the cohomology class associated to every periodic wave by considering degrees indicates whether an evasion path exists or not.