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 February 2nd, 2019, 09:24 AM #1 Newbie   Joined: Jan 2019 From: italy Posts: 6 Thanks: 0 Exercise on Tangent bundle Hi everybody, I have to verify that $S'\times S^2$ doesn't have a frame. That's what I would do: $S'$ has a frame so $T_S'= S'\times \mathbb R$. $S^2$ doesn't have a frame so $T_{S^2}\ne S^2 \times \mathbb {R}^2$. $S'\times S^2$ has a frame if and only if $T_{S'\times S^2}= S'\times S^2 \times \mathbb {R}^3$. But since $T_{S^2}\ne S^2 \times \mathbb {R}^2$ that's impossibile. Am I right? thank you all  Tags bundle, diffeomorphism, exercise, frame, tangent, tangent bundle Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ManosG Real Analysis 3 March 26th, 2013 02:11 PM Aqil Economics 0 November 17th, 2009 08:14 AM bortkiew Real Analysis 1 October 27th, 2009 09:14 AM me Trigonometry 3 January 31st, 2008 09:30 AM

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