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29. ( )
Theorem(W.)
Let M be a 1-connected space with dim(π∗(M) ⊗ Q) < ∞. Assume
∃ F → M → B fibration satisfying
• F and B are 1-connected
• B is rationally homotopy equivalent to S2n+1
• ∂ ⊗ 1 = 0: π2n+1(B) ⊗ Q → π2n(F) ⊗ Q
Then the loop coproduct on LM is trivial.
• A ⇒ B (Assume A. Then B.)
A: B:
• A, B
•
( ) 2017 7 19 3 / 10
“
2017-07-19 有理ホモトピー論とコンピュータ @wktkshn

30. • F and B are 1-connected
• B is rationally homotopy equivalent to S2n+1
• ∂ ⊗ 1 = 0: π2n+1(B) ⊗ Q → π2n(F) ⊗ Q
Then the loop coproduct on LM is trivial.
• A ⇒ B (Assume A. Then B.)
A: B:
• A, B
•
( ) 2017 7 19 3 / 10

31. ]ie°z -
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32. committer wanted!
SwiftyMath