Open-Closed String Topology via Fat Graphs
代数拓扑
2007-05-23 v1 几何拓扑
摘要
Given a smooth closed manifold M with a family {L_i} of closed submanifolds, we consider the free loop space LM and the spaces PM(L_i,L_j) of open strings (paths g:[0,1]->M with g(0) in L_i, and g(1) in L_j). We construct string topology operations resulting in an open-closed TQFT on the family (h_*(LM),h_*(PM(L_i,L_j)) which extends the known string topology TQFT on h_*(LM). Here, h_* is a multiplicative generalized homology theory supporting orientations for M and the L_i. To construct the operations, we introduce the notion of open-closed fat graph, generalizing fat graphs to the open-closed setting.
引用
@article{arxiv.math/0606512,
title = {Open-Closed String Topology via Fat Graphs},
author = {Antonio Ramirez},
journal= {arXiv preprint arXiv:math/0606512},
year = {2007}
}
备注
36 pages