In what dimensions are PL and Diff equivalent?
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I have read in different places, that for $nleq 4$, PL and Diff are equivalent (passing through PDIFF). I believe Milnor gave an example of the inequivalence for $n=7$. What about for $n=5$ or $n=6$? Are there examples of PL manifolds which are not smoothable?
algebraic-topology manifolds differential-topology smooth-manifolds
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
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add a comment |
$begingroup$
I have read in different places, that for $nleq 4$, PL and Diff are equivalent (passing through PDIFF). I believe Milnor gave an example of the inequivalence for $n=7$. What about for $n=5$ or $n=6$? Are there examples of PL manifolds which are not smoothable?
algebraic-topology manifolds differential-topology smooth-manifolds
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
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1
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Maybe relevant: mathoverflow.net/questions/96670/….
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 14 '18 at 20:53
add a comment |
$begingroup$
I have read in different places, that for $nleq 4$, PL and Diff are equivalent (passing through PDIFF). I believe Milnor gave an example of the inequivalence for $n=7$. What about for $n=5$ or $n=6$? Are there examples of PL manifolds which are not smoothable?
algebraic-topology manifolds differential-topology smooth-manifolds
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
$endgroup$
I have read in different places, that for $nleq 4$, PL and Diff are equivalent (passing through PDIFF). I believe Milnor gave an example of the inequivalence for $n=7$. What about for $n=5$ or $n=6$? Are there examples of PL manifolds which are not smoothable?
algebraic-topology manifolds differential-topology smooth-manifolds
algebraic-topology manifolds differential-topology smooth-manifolds
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
asked Dec 14 '18 at 19:36
Michael ShumateMichael Shumate
13711
13711
1
$begingroup$
Maybe relevant: mathoverflow.net/questions/96670/….
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 14 '18 at 20:53
add a comment |
1
$begingroup$
Maybe relevant: mathoverflow.net/questions/96670/….
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 14 '18 at 20:53
1
1
$begingroup$
Maybe relevant: mathoverflow.net/questions/96670/….
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 14 '18 at 20:53
$begingroup$
Maybe relevant: mathoverflow.net/questions/96670/….
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 14 '18 at 20:53
add a comment |
1 Answer
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A more qeneral question is References on the relations between Top, Diff and PL. It gives a reference to https://mathoverflow.net/q/96670 which gives a complete (positive) answer for $n =5, 6$.
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
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$begingroup$
A more qeneral question is References on the relations between Top, Diff and PL. It gives a reference to https://mathoverflow.net/q/96670 which gives a complete (positive) answer for $n =5, 6$.
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
$endgroup$
add a comment |
$begingroup$
A more qeneral question is References on the relations between Top, Diff and PL. It gives a reference to https://mathoverflow.net/q/96670 which gives a complete (positive) answer for $n =5, 6$.
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
$endgroup$
add a comment |
$begingroup$
A more qeneral question is References on the relations between Top, Diff and PL. It gives a reference to https://mathoverflow.net/q/96670 which gives a complete (positive) answer for $n =5, 6$.
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
$endgroup$
A more qeneral question is References on the relations between Top, Diff and PL. It gives a reference to https://mathoverflow.net/q/96670 which gives a complete (positive) answer for $n =5, 6$.
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
answered Dec 14 '18 at 22:52
Paul FrostPaul Frost
12.6k31035
12.6k31035
add a comment |
add a comment |
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Maybe relevant: mathoverflow.net/questions/96670/….
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 14 '18 at 20:53