Application Of Homology To Spectral Sequence And Digital Topology

Homology theory has a universal use in some branches of science,this paper mainly discusses some applications in spectral sequence and digital topology.The former mainly involves the discussion of E2-term in Adams spectral sequence,the latter discusses the digital topological characteristics of specific digital closed surface and digital cube.Firstly,by using the May spectral sequence,the elements b1,k0δs+4(0<s<p-4)in the classical Adams spectral sequence are nontrivial.Secondly,k-adjacent digital j-persistent homology is defined by k-adjacent digital simplicial homology.The digital closed surface,digital wedge sum and digital connected sum are introduced.And then,the j-persistent homology groups,j-persistent Betti numbers and j-persistent Euler characteristics of MSS’18 ∨ MSS’18,MSS’18 V MSS18 and MSS18#MSSl8 will be computed respectively.In addition,the digital cubical homology is established in K-product topology space,and it computes the digital cubical homology group of[0,1]z x[0,1]z x[0,2]z and gets the digital cubical homology group of[0,1]z x[0,1]z x[0,n]z(n≥2).