Open-Closed String Topology via Fat Graphs
Antonio Ramirez
Abstract
Given a smooth closed manifold M with a family Li of closed submanifolds, we consider the free loop space LM and the spaces PM(Li,Lj) of open strings (paths g:[0,1]->M with g(0) in Li, and g(1) in Lj). We construct string topology operations resulting in an open-closed TQFT on the family (h*(LM),h*(PM(Li,Lj)) which extends the known string topology TQFT on h*(LM). Here, h* is a multiplicative generalized homology theory supporting orientations for M and the Li. To construct the operations, we introduce the notion of open-closed fat graph, generalizing fat graphs to the open-closed setting.
Create a lesson
Related papers
Koszul duality and Morita categories
Max Blans
Persistence Meets Resistance: Doubling Down on Hardness
Benedikt Kolbe, Tim Mayr
On orientability, Poincaré duality, and connectivity of GKM graphs
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
Local Bousfield classes via homological support
Tobias Barthel, Natalia Castellana, Drew Heard et al.
Coordinate-Deletion Bundles from Composition Algebras: Hopf Defects, KO-Classes, and Real Projective Space
Marina Palaisti
The product rule in Goodwillie calculus
Max Blans, Thomas Blom