A Generalized Discrete Morse-Floer Theory  

作　　者：Jürgen Jost Sylvia Yaptieu 

机构地区：[1]Max Planck Institute for Mathematics in the Sciences,Inselstrasse 22,04103 Leipzig,Germany [2]Santa Fe Institute for the Sciences of Complexity,Santa Fe,NM 87501,USA

出　　处：《Communications in Mathematics and Statistics》2019年第3期225-252,共28页数学与统计通讯（英文）

基　　金：funding provided by Max Planck Society;supported by a stipend from the InternationalMax Planck Research School(IMPRS)“Mathematics in the Sciences.”。

摘　　要：Forman has developed a version of discrete Morse theory that can be understood in terms of arrow patterns on a(simplicial,polyhedral or cellular)complex without closed orbits,where each cell may either have no arrows,receive a single arrow from one of its facets,or conversely,send a single arrow into a cell of which it is a facet.By following arrows,one can then construct a natural Floer-type boundary operator.Here,we develop such a construction for arrow patterns where each cell may support several outgoing or incoming arrows(but not both),again in the absence of closed orbits.Our main technical achievement is the construction of a boundary operator that squares to 0 and therefore recovers the homology of the underlying complex.

关 键 词：CW complex Boundary operator Floer theory Poincarépolynomial Betti number Discrete Morsetheory Discrete Morse-Floertheory Conleytheory 

分 类 号：O17[理学—数学]