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Post by Admin on Mar 16, 2017 6:56:47 GMT
Gary
I think that $h(\Gamma)$ and $h(\widetilde{\Gamma})$ should be $h(\Gamma_a)$ and $h(\widetilde{\Gamma}_a)$. Do you agree?
Vasco
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Gary
GaryVasco
Posts: 3,352 
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Post by Gary on Mar 16, 2017 15:12:57 GMT
Gary I think that $h(\Gamma)$ and $h(\widetilde{\Gamma})$ should be $h(\Gamma_a)$ and $h(\widetilde{\Gamma}_a)$. Do you agree? Vasco Vasco, Yes, it looks like the $a$'s were inadvertently left out. Gary |
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Post by mondo on May 28, 2023 23:30:08 GMT
Gary I think that $h(\Gamma)$ and $h(\widetilde{\Gamma})$ should be $h(\Gamma_a)$ and $h(\widetilde{\Gamma}_a)$. Do you agree? Vasco I don't think so, $\Gamma_a$ is a loop around $a$ - a preimage of $p$ hence on the right hand side of figure [10] it is a loop around the image of $a$ - $p$ so either $h(\Gamma)$ or $h(\Gamma_p)$ to be specific. |
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Post by Admin on May 29, 2023 13:11:01 GMT
Gary I think that $h(\Gamma)$ and $h(\widetilde{\Gamma})$ should be $h(\Gamma_a)$ and $h(\widetilde{\Gamma}_a)$. Do you agree? Vasco I don't think so, $\Gamma_a$ is a loop around $a$ - a preimage of $p$ hence on the right hand side of figure [10] it is a loop around the image of $a$ - $p$ so either $h(\Gamma)$ or $h(\Gamma_p)$ to be specific. Mondo The loops on the right hand side of figure 10 on page 348 are the result of mapping the points on the loops on the left hand side using the mapping function $h$ and so it makes perfect sense that the loops on the right are called $h(\Gamma_a)$ and $h(\widetilde{\Gamma}_a)$. Didn't you notice that in the mathematics immediately below figure 10 that this is exactly what Needham does? Therefore I disagree with what you say above. Vasco |
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Post by mondo on May 29, 2023 19:36:56 GMT
I don't think so, $\Gamma_a$ is a loop around $a$ - a preimage of $p$ hence on the right hand side of figure [10] it is a loop around the image of $a$ - $p$ so either $h(\Gamma)$ or $h(\Gamma_p)$ to be specific. Mondo The loops on the right hand side of figure 10 on page 348 are the result of mapping the points on the loops on the left hand side using the mapping function $h$ and so it makes perfect sense that the loops on the right are called $h(\Gamma_a)$ and $h(\widetilde{\Gamma}_a)$. Didn't you notice that in the mathematics immediately below figure 10 that this is exactly what Needham does? Therefore I disagree with what you say above. Vasco I agree, when confronted with the math below it doesn't make sense. |
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