Steply cohomology modules of finite partially ordered sets
Caijun Zhou · Journal of Shanghai Normal University · 2009
This paper mainly studies the twice-steply cohomology modules of finite partially ordered sets.Some properties of these modules are discussed.Two examples are given which show that the properties of such modules depend not only on the topological properties,but also on the combinatorial properties of the partially ordered sets.Two results are obtained on follows:(i) Let P be a finite partially ordered set,let x1,x2 be any two elements of P,and d2 be the sum of all the elements except x1,x2 in P,if x1 x2=0,then P is cyclic if and only if Hx1+x2Hd2(P)=0;(ii) Let P be a finite cone partially ordered set,P=P1∪ P2,P1∩ P2= and d1,d2 be the sum of all the elements in P1,P2 separately.Then Hd1Hd2(P)=0.