Giải thức tối tiểu cho đại số steenrod A_3 tại những bậc trong t≤30
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Abstract
An important issue in the study of the classification problem with the type homotopy of topological spaces is the identification of the homotopy group, especially the stable homotopy group of spheres. Adams spectral sequence will be converged on the 3-torsion component of the stable homotopy group of spheres π_*^S (S^0 ). The E_2-term of the Adams spectral sequence is cohomology of the mod 3 Steenrod algebra "Ex" "t" _A^(*,*) (F_3,F_3 ). To compute the E_2-term of the Adams spectral sequence, we need to compute "Ex" "t" _A^(*,*) (F_3,F_3 )=H^(*,*) ("Hom" (P_*,F_3 ),δ) for any free A -module resolution of F_3. In this paper, a free resolution P_* for internal degrees t≤30 was constructed.
Tóm tắt
Một vấn đề quan trọng trong nghiên cứu bài toán phân loại kiểu đồng luân của các không gian tôpô là xác định nhóm đồng luân, đặc biệt là nhóm đồng luân ổn định của mặt cầu. Dãy phổ Adams hội tụ về thành phần 3-xoắn của nhóm đồng luân ổn định của mặt cầu π_*^S (S^0 ). Trang E_2 của dãy phổ Adams chính là đối đồng điều của đại số Steenrod "Ex" "t" _A^(*,*) (F_3,F_3 ). Để tính trang E_2 của dãy phổ Adams, ta cần tính "Ex" "t" _A^(*,*) (F_3,F_3 )=H^(*,*) ("Hom" (P_*,F_3 ),δ) cho giải thức A -mô đun tự do bất kỳ của F_3. Trong bài báo này, giải thức tự do〖 P〗_* đối với những bậc trong t≤30 được xây dựng.
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Tài liệu tham khảo
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