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Is every fibration locally trivial? If there is counter example, what is different between locally trivial different and non one ? Or Does it have condition for determine a fibration is locally trivial?

user10354138
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Ramtin.VA
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    When you say "locally trivial" do you mean "locally isomorphic to a product fibration" or "locally homotopic to a product fibration" ? – Maxime Ramzi Jun 24 '19 at 16:20
  • @Max I mean “locally diffeomorphic to a product fibration “ , my main problem is that I have fibration $\pi:M\longrightarrow T^2$ ,the I want to prove that induced homomorphism of cohomology group is injective, so I am going to khnow is it related to locally trivial property of fibration. – Ramtin.VA Jun 24 '19 at 16:30
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    Oh so you're asking about the smooth setting. I don't know about that, but in the continuous setting (replacing "diffeomorphic" by "homeomorphic") it's not true – Maxime Ramzi Jun 24 '19 at 16:32
  • See this answer for example. – user10354138 Jun 24 '19 at 17:27
  • @user10354138 it mean if smooth fibration is compact with compact base space is fiber bundle? – Ramtin.VA Jun 24 '19 at 17:48

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