Mixing
Discrete Morse Function for $n$-simplex
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I am trying to find a "useful" discrete Morse function for the $n$-simplex.
According to (https://www.emis.de/journals/SLC/wpapers/s48forman.pdf page 12), a possible discrete Morse function is $f(sigma)=dimsigma$.
However, this type of discrete Morse function is typically "useless".
Since a $n$-simplex is contractible to a point, I am looking for a discrete Morse function $f$ that reflects this information. That is, we should be able to "collapse" the $n$-simplex to a point according to $f$.
For small $n$, I am able to find such discrete Morse functions. However for general $n$, how do we define $f$ systematically?
Thanks a lot.
algebraic-topology differential-topology simplex morse-theory
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
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add a comment |
$begingroup$
I am trying to find a "useful" discrete Morse function for the $n$-simplex.
According to (https://www.emis.de/journals/SLC/wpapers/s48forman.pdf page 12), a possible discrete Morse function is $f(sigma)=dimsigma$.
However, this type of discrete Morse function is typically "useless".
Since a $n$-simplex is contractible to a point, I am looking for a discrete Morse function $f$ that reflects this information. That is, we should be able to "collapse" the $n$-simplex to a point according to $f$.
For small $n$, I am able to find such discrete Morse functions. However for general $n$, how do we define $f$ systematically?
Thanks a lot.
algebraic-topology differential-topology simplex morse-theory
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
$endgroup$
add a comment |
$begingroup$
I am trying to find a "useful" discrete Morse function for the $n$-simplex.
According to (https://www.emis.de/journals/SLC/wpapers/s48forman.pdf page 12), a possible discrete Morse function is $f(sigma)=dimsigma$.
However, this type of discrete Morse function is typically "useless".
Since a $n$-simplex is contractible to a point, I am looking for a discrete Morse function $f$ that reflects this information. That is, we should be able to "collapse" the $n$-simplex to a point according to $f$.
For small $n$, I am able to find such discrete Morse functions. However for general $n$, how do we define $f$ systematically?
Thanks a lot.
algebraic-topology differential-topology simplex morse-theory
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
$endgroup$
I am trying to find a "useful" discrete Morse function for the $n$-simplex.
According to (https://www.emis.de/journals/SLC/wpapers/s48forman.pdf page 12), a possible discrete Morse function is $f(sigma)=dimsigma$.
However, this type of discrete Morse function is typically "useless".
Since a $n$-simplex is contractible to a point, I am looking for a discrete Morse function $f$ that reflects this information. That is, we should be able to "collapse" the $n$-simplex to a point according to $f$.
For small $n$, I am able to find such discrete Morse functions. However for general $n$, how do we define $f$ systematically?
Thanks a lot.
algebraic-topology differential-topology simplex morse-theory
algebraic-topology differential-topology simplex morse-theory
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
asked Jan 30 at 10:25
yoyosteinyoyostein
8,160104073
8,160104073
add a comment |
add a comment |
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