I know that the solution to this is simple, but for the life of me I just can't see it. I know the homotopy from f to g is required but I'm not sure how to put it in there. Any help would be appreciated.
f,g: X $\rightarrow $Y homeomorphisms that are homotopic. Then $f^{-1}$ and $g^{-1}$ are homotopic.
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general-topology
homotopy-theory
1 Answers
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There exists $H_t:X\rightarrow Y, t\in [0,1]$ such that $H_0=f, H_1=g$
Consider $W_t=g^{-1}H_tf^{-1}, W_0=g^{-1}ff^{-1}=g^{-1}$. $W_1=g^{-1}gf^{-1}=f^{-1}$.
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0Thanks! I knew it had to be a "conjugation" like that. – 2017-01-29