Λ࣋ͭ -Ͱ͋Γɼ - ༨ੵ ͱ ༨୯Ґ Λ࣋ͭ -༨Ͱ͋Γɼ - Frobenius ؔࣜɿ Λຬͨ͢ͱ͖ɼ Λ ্ͷ Frobenius ͱ͍͏ɽ k A m : A ⊗ A → A ι : k → A k Δ : A → A ⊗ A ϵ : A → k k Δ ∘ m = (id ⊗ m) ∘ (Δ ⊗ id) = (m ⊗ id) ∘ (id ⊗ Δ) A k
¥72213 Is D8 100 1 10 add IB Ind 8.8 000 010 10 I 11 1 IDE did 001 Of 1 3 . At # Esa III 's a # ¥72213 Is D8 100 1 10 add IB Ind 8.8 000 010 10 I 11 1 IDE did 001 Of 1 Oo §??tE ¥¥¥¥o←s NFSHF
¥72213 Is D8 100 1 10 add IB Ind 8.8 000 010 10 I 11 1 IDE did 001 Of 1 3 . At # Esa III 's a # ¥72213 Is D8 100 1 10 add IB Ind 8.8 000 010 10 I 11 1 IDE did 001 Of 1 Oo §??tE ¥¥¥o←s TQMJU
¥72213 #*.€as ***e**¥EE¥a*⇐e¥ Edi did w 'SPCFOJVT ʹΑΓఆ·Δ52'5 ͰϕΫτϧ ۭؒͷݍʹҠ͢ʂ A = ℚ[X]/(X2) ℱ ⟶ ℱ A⊗3 A⊗2 A⊗2 A⊗2 A A A A⊗2 m m m m m m m m m Δ Δ Δ Cob2 Vectℚ
• Khovanov homology ʹ͍ͭͯ - େ௬ʰ݁ͼͷෆมྔʱɼڞཱग़൛ - D. Bar-Natan, On Khovanov's categorification of the Jones polynomial • Frobenius ͱ TQFT ʹ͍ͭͯ - J. Kock, Frobenius algebras and 2D topological quantum field theories