Mathematics Colloquia and Seminars
Generalized Property R and trisections of the 4-sphereGeometry/Topology
|Speaker:||Alex Zupan, Univ of Nebraska|
|Start time:||Tue, May 10 2016, 1:10PM|
Waldhausen's Theorem implies that any handle decomposition of the 3-sphere can be simplified without introducing additional handles. The analogue in dimension 4 is unknown, but it is widely believed that there are decompositions of the standard smooth 4-sphere which require additional pairs of canceling handles before they admit simplification. For some decompositions, this problem reduces to a 3-dimensional conjecture known as the Generalized Property R Conjecture (GPRC). We can use trisections in this setting for a two-fold purpose: We resolve a weakening of the GPRC in certain cases, and we also give a new perspective on prominent potential counterexamples to the GPRC, describing connections to potential well-known counterexamples to the Andrews-Curtis Conjecture.