Unreadable lines of Milnor's bookDefinition of a 4-cobordism with boundaryReference request : Study of...
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Unreadable lines of Milnor's book
Definition of a 4-cobordism with boundaryReference request : Study of Differential topology post Milnor's bookLemma about Brouwer degree in Milnor's bookCollar neighborhood theorem- CobordismProblem 5 of Milnor's “Topology From The Differentiable Viewpoint”Problem in Milnor's proof of h-cobordism theoremLimitive result in constructing cobordisms for 3-manifoldsPontryagin-Thom construction references for homotopy groups of spheresA Lemma from Milnor's Topology from the Differentiable Viewpoint
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What are the (exact sentence of) Unreadable lines of the following images of Milnor's Lecture on h-cobordism theorem? (pages number: 28, 30, 15 respectively)
differential-topology cobordism milnor-books
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
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|
show 1 more comment
$begingroup$
What are the (exact sentence of) Unreadable lines of the following images of Milnor's Lecture on h-cobordism theorem? (pages number: 28, 30, 15 respectively)
differential-topology cobordism milnor-books
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
$endgroup$
$begingroup$
Why do you think there must be lines missing, and where?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
It is unreadable and not missing. the question is vague?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G: Do you mean the half lines where you have cropped the pictures?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
@HenningMakholm, End of each picture.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@NickD, "... with respect to the Morse function f," I know, but does f has any indices or something else?
$endgroup$
– C.F.G
9 hours ago
|
show 1 more comment
$begingroup$
What are the (exact sentence of) Unreadable lines of the following images of Milnor's Lecture on h-cobordism theorem? (pages number: 28, 30, 15 respectively)
differential-topology cobordism milnor-books
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
$endgroup$
What are the (exact sentence of) Unreadable lines of the following images of Milnor's Lecture on h-cobordism theorem? (pages number: 28, 30, 15 respectively)
differential-topology cobordism milnor-books
differential-topology cobordism milnor-books
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
edited 7 hours ago
C.F.G
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
asked 9 hours ago
C.F.GC.F.G
1,8521 gold badge8 silver badges26 bronze badges
1,8521 gold badge8 silver badges26 bronze badges
$begingroup$
Why do you think there must be lines missing, and where?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
It is unreadable and not missing. the question is vague?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G: Do you mean the half lines where you have cropped the pictures?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
@HenningMakholm, End of each picture.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@NickD, "... with respect to the Morse function f," I know, but does f has any indices or something else?
$endgroup$
– C.F.G
9 hours ago
|
show 1 more comment
$begingroup$
Why do you think there must be lines missing, and where?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
It is unreadable and not missing. the question is vague?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G: Do you mean the half lines where you have cropped the pictures?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
@HenningMakholm, End of each picture.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@NickD, "... with respect to the Morse function f," I know, but does f has any indices or something else?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
Why do you think there must be lines missing, and where?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
Why do you think there must be lines missing, and where?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
It is unreadable and not missing. the question is vague?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
It is unreadable and not missing. the question is vague?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G: Do you mean the half lines where you have cropped the pictures?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
@C.F.G: Do you mean the half lines where you have cropped the pictures?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
@HenningMakholm, End of each picture.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@HenningMakholm, End of each picture.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@NickD, "... with respect to the Morse function f," I know, but does f has any indices or something else?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@NickD, "... with respect to the Morse function f," I know, but does f has any indices or something else?
$endgroup$
– C.F.G
9 hours ago
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
p. 28 "with respect to the Morse function $f$, is well-defined (i.e., independent of choice of $f$ and $p$)."
p. 30 "(2) $(vec{x},vec{y})$ lies on the orthogonal trajectory which passes through the point $(ucoshtheta,vsinh theta)$."
p. 15 "$N_1$ of $f_1$, $N_1subset N$, so that any function in $N_1$ is still good on $C_1$. This completes the first stage."
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
$endgroup$
$begingroup$
Thanks. but for p. 28, I need words before "independent of choice". Thanks also for noticing hidden text "$f$ and $p$". I never see this.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G I edited my answer. Let me know if you need further help.
$endgroup$
– Robert Z
9 hours ago
add a comment |
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$begingroup$
p. 28 "with respect to the Morse function $f$, is well-defined (i.e., independent of choice of $f$ and $p$)."
p. 30 "(2) $(vec{x},vec{y})$ lies on the orthogonal trajectory which passes through the point $(ucoshtheta,vsinh theta)$."
p. 15 "$N_1$ of $f_1$, $N_1subset N$, so that any function in $N_1$ is still good on $C_1$. This completes the first stage."
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
$endgroup$
$begingroup$
Thanks. but for p. 28, I need words before "independent of choice". Thanks also for noticing hidden text "$f$ and $p$". I never see this.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G I edited my answer. Let me know if you need further help.
$endgroup$
– Robert Z
9 hours ago
add a comment |
$begingroup$
p. 28 "with respect to the Morse function $f$, is well-defined (i.e., independent of choice of $f$ and $p$)."
p. 30 "(2) $(vec{x},vec{y})$ lies on the orthogonal trajectory which passes through the point $(ucoshtheta,vsinh theta)$."
p. 15 "$N_1$ of $f_1$, $N_1subset N$, so that any function in $N_1$ is still good on $C_1$. This completes the first stage."
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
$endgroup$
$begingroup$
Thanks. but for p. 28, I need words before "independent of choice". Thanks also for noticing hidden text "$f$ and $p$". I never see this.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G I edited my answer. Let me know if you need further help.
$endgroup$
– Robert Z
9 hours ago
add a comment |
$begingroup$
p. 28 "with respect to the Morse function $f$, is well-defined (i.e., independent of choice of $f$ and $p$)."
p. 30 "(2) $(vec{x},vec{y})$ lies on the orthogonal trajectory which passes through the point $(ucoshtheta,vsinh theta)$."
p. 15 "$N_1$ of $f_1$, $N_1subset N$, so that any function in $N_1$ is still good on $C_1$. This completes the first stage."
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
$endgroup$
p. 28 "with respect to the Morse function $f$, is well-defined (i.e., independent of choice of $f$ and $p$)."
p. 30 "(2) $(vec{x},vec{y})$ lies on the orthogonal trajectory which passes through the point $(ucoshtheta,vsinh theta)$."
p. 15 "$N_1$ of $f_1$, $N_1subset N$, so that any function in $N_1$ is still good on $C_1$. This completes the first stage."
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
edited 9 hours ago
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
answered 9 hours ago
Robert ZRobert Z
111k10 gold badges78 silver badges153 bronze badges
111k10 gold badges78 silver badges153 bronze badges
$begingroup$
Thanks. but for p. 28, I need words before "independent of choice". Thanks also for noticing hidden text "$f$ and $p$". I never see this.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G I edited my answer. Let me know if you need further help.
$endgroup$
– Robert Z
9 hours ago
add a comment |
$begingroup$
Thanks. but for p. 28, I need words before "independent of choice". Thanks also for noticing hidden text "$f$ and $p$". I never see this.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G I edited my answer. Let me know if you need further help.
$endgroup$
– Robert Z
9 hours ago
$begingroup$
Thanks. but for p. 28, I need words before "independent of choice". Thanks also for noticing hidden text "$f$ and $p$". I never see this.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
Thanks. but for p. 28, I need words before "independent of choice". Thanks also for noticing hidden text "$f$ and $p$". I never see this.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G I edited my answer. Let me know if you need further help.
$endgroup$
– Robert Z
9 hours ago
$begingroup$
@C.F.G I edited my answer. Let me know if you need further help.
$endgroup$
– Robert Z
9 hours ago
add a comment |
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$begingroup$
Why do you think there must be lines missing, and where?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
It is unreadable and not missing. the question is vague?
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@C.F.G: Do you mean the half lines where you have cropped the pictures?
$endgroup$
– Henning Makholm
9 hours ago
$begingroup$
@HenningMakholm, End of each picture.
$endgroup$
– C.F.G
9 hours ago
$begingroup$
@NickD, "... with respect to the Morse function f," I know, but does f has any indices or something else?
$endgroup$
– C.F.G
9 hours ago