If X is path connected how may i show that the reduced Suspension $\Sigma $ X is then simply connected. I cannot seem to picture this construction
Simply connected reduced suspension on path connected X
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algebraic-topology
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2Do you know the seifert can kampen theorem? – 2012-09-13
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0Whilst I thought it was true immediately by the Freudenthal suspension theorem, there are a serious of posts by Tom Goodwillie http://www.lehigh.edu/~dmd1/tg26, http://www.lehigh.edu/~dmd1/tg27, http://www.lehigh.edu/~dmd1/tg28 that suggests it might not (always be true). Although I can't see any flaw in the argument provided below... – 2012-09-13
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0@JuanS: I haven't read the posts in detail, but in the first one the counterexample he produces involved the Hawaiian earring which does not satisfy the hypotheses of Freudenthal's suspension theorem. – 2014-03-10