Uniform TitleThe multiplihedra in Lagrangian Floer theory
NameMau, Sikimeti Luisa (author), Woodward, Chris (chair), Weibel, Charles (internal member), Buch, Anders (internal member), Albers, Peter (outside member), Rutgers University, Graduate School - New Brunswick,
DescriptionWe apply the quilted Floer theory of Wehrheim and Woodward to families of quilted surfaces parametrized by the Stasheff multiplihedra. Our approach is modeled on the construction of the Fukaya category, which applies Floer theory to families of pointed Riemann surfaces parametrized by the associahedra. First, we show that the multiplihedra are realized as a moduli space of quilted disks. Using the quilted disks we define the moduli space of pseudoholomorphic quilted disks, which under suitable transversality assumptions are smooth manifolds. Then we prove a gluing theorem relating ``broken'' tuples of pseudoholomorphic quilted disks with boundaries of one-parameter familes of pseudoholomorphic quilted disks.
NoteIncludes bibliographical references (p. 171-172).
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.