Using the stratifications of Deligne–Mumford moduli spaces M_(g,n) indexed by stable graphs,we introduce a partially ordered set of stable graphs by defining a partial ordering on the set of connected stable graphs o...Using the stratifications of Deligne–Mumford moduli spaces M_(g,n) indexed by stable graphs,we introduce a partially ordered set of stable graphs by defining a partial ordering on the set of connected stable graphs of genus g with n external edges.By modifying the usual definition of zeta function and Möbius function of a poset,we introduce generalized(Q-valued)zeta function and generalized(Q-valued)Möbius function of the poset of stable graphs.We use them to proved a generalized Möbius inversion formula for functions on the poset of stable graphs.Two applications related to duality in earlier work are also presented.展开更多
基金Supported by NSFC(Grant Nos.12371254,11890662,12061131014)。
文摘Using the stratifications of Deligne–Mumford moduli spaces M_(g,n) indexed by stable graphs,we introduce a partially ordered set of stable graphs by defining a partial ordering on the set of connected stable graphs of genus g with n external edges.By modifying the usual definition of zeta function and Möbius function of a poset,we introduce generalized(Q-valued)zeta function and generalized(Q-valued)Möbius function of the poset of stable graphs.We use them to proved a generalized Möbius inversion formula for functions on the poset of stable graphs.Two applications related to duality in earlier work are also presented.
