Dimensional Manifold In The Matrix And The Chain Polynomial Calculation,

In　this　paper　we　first　introduce　the　linear　skein　theory,　then　get　a　module Vm (it　is　also　an　algebra　which　is　generated　by　the　elements　{ I_m , e₁ , e₂ L ,e_m-1)}.　We　found　a　bilinear　form　of　V m by　Markov　trace　and　it　is　also　a　product　on　Temperly-Lieb　algebra Vm .thus,　we　can　get　its　basis　matrix B ( m ).we　discuss　mainly　basis　matrix　B ( m )and　compute　det B ( m ) = Δ₁^(m-1)2+1Δ₂^m-1,where Δ_i is　the　chebyshev　polynomial　[2],[3].In　order　to　　give　the　reader　a　clear　and　straight　understand　of　V_m 　,we　give　a　simple　example　V₃ 　and　get　some　special　but　good　propositions.　Meantime,　we　induce　a　linear　map　from　V_m 　to　U (it　is　complex　vector　space　of　link　diagrams　of　closed　curves　in　an　annulus　module　relation)　by　considering　U 's　module　relation　is　similar　to　V_m 's　and　build　a　relation　between　Markov　trace　and　Kauffman　bracket　polynomial.　We　find　recursive　formulas　(such　as　T_{i + j} , ( x_m )ⁱ,x_m,　ect)　for　computing　some　link　polynomials　by　defining　two　self-maps　cand　τ　of　V_m (or　U ).　Hence,　one　can　compute　their　Kauffman　bracket-polynomial.