Floer Homology:From Generalized Morse–Smale Dynamical Systems to Forman’s Combinatorial Vector Fields  

作　　者：Marzieh Eidi Jürgen Jost 

机构地区：[1]Max-Planck Institute for Mathematics in the Sciences,Leipzig,Germany [2]Santa Fe Institute,Santa Fe,NM,USA

出　　处：《Communications in Mathematics and Statistics》2024年第4期695-720,共26页数学与统计通讯（英文）

摘　　要：We construct a Floer type boundary operator for generalised Morse–Smale dynamical systems on compact smooth manifolds by counting the number of suitable flow lines between closed(both homoclinic and periodic)orbits and isolated critical points.The same principle works for the discrete situation of general combinatorial vector fields,defined by Forman,on CW complexes.We can thus recover the Z2 homology of both smooth and discrete structures directly from the flow lines(V-paths)of our vector field.

关 键 词：FIELD MORSE FLOW 

分 类 号：O17[理学—数学]