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,...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.展开更多
This article studies the Floer theory of Landau-Ginzburg （LG） model on C^n. We perturb the Kahler form within a fixed Kahler class to guarantee the transversal intersection of Lefschetz thimbles. The C^0 estimate fo...This article studies the Floer theory of Landau-Ginzburg （LG） model on C^n. We perturb the Kahler form within a fixed Kahler class to guarantee the transversal intersection of Lefschetz thimbles. The C^0 estimate for solutions of the LG Floer equation can be derived then by our analysis tools. The Fredholm property is guaranteed by all these results.展开更多
基金funding provided by Max Planck Societysupported by a stipend from the InternationalMax Planck Research School(IMPRS)“Mathematics in the Sciences.”。
文摘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.
基金Acknowledgements The author would like to thank his advisor, Gang Tian, for his great help and long-lasting support to carry on this research. Many thanks to Huijun Fan and Yongbin Ruan for sharing many of their insights into the study of Floer theory of LG model. Many thanks to Yong-Guen Oh for rich knowledge of Floer theory of Lagrangian intersection as well as his suggestions. Thanks also goes to Yefeng Shen, Yalong Shi, Dongning Wang, and Ke Zhu for helpful discussion. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11171143）.
文摘This article studies the Floer theory of Landau-Ginzburg （LG） model on C^n. We perturb the Kahler form within a fixed Kahler class to guarantee the transversal intersection of Lefschetz thimbles. The C^0 estimate for solutions of the LG Floer equation can be derived then by our analysis tools. The Fredholm property is guaranteed by all these results.
