Russel Avdek

Title: A closed, tight contact 3-manifold with vanishing contact homology

Abstract: Contact homology (CH) is an invariant which assigns a differential
graded algebra to each closed contact manifold. While this invariant
shares some formal properties with Heegaard-Floer homology, CH is
comparatively not well-understood due to a current lack of
computational techniques. In this talk, we will describe the first
example of a closed, tight contact 3-manifold whose CH is the zero
algebra. In proving that CH=0 for this contact manifold, we will
summarize some computational tools which relate surgeries and
cobordisms to dynamical systems and holomorphic curves in a
combinatorial fashion.