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John Klein
John Klein
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Perhaps worth noting here:

There is an old open conjecture, the Hirsch conjecture, which says that a stably parallelizable (closed) smooth $n$-manifold $M$ always embeds in $\Bbb R^{[(3/2)n]}$ (approximately). The conjecture has been verified when $M$ is $[n/4]$-connected.

A compact Lie group is parallelizable so, if the conjecture is true, then the top cell will split off after approximately $[n/2]$-suspensions if the Lie group has dimension $n$.

Perhaps worth noting here:

There is an old open conjecture, the Hirsch conjecture, which says that a stably parallelizable (closed) smooth $n$-manifold always embeds in $\Bbb R^{[(3/2)n]}$ (approximately). The conjecture has been verified when $M$ is $[n/4]$-connected.

A compact Lie group is parallelizable so, if the conjecture is true, then the top cell will split off after approximately $[n/2]$-suspensions if the Lie group has dimension $n$.

Perhaps worth noting here:

There is an old open conjecture, the Hirsch conjecture, which says that a stably parallelizable (closed) smooth $n$-manifold $M$ always embeds in $\Bbb R^{[(3/2)n]}$ (approximately). The conjecture has been verified when $M$ is $[n/4]$-connected.

A compact Lie group is parallelizable so, if the conjecture is true, then the top cell will split off after approximately $[n/2]$-suspensions if the Lie group has dimension $n$.

Source Link
John Klein
John Klein
  • 18.8k
  • 53
  • 109

Perhaps worth noting here:

There is an old open conjecture, the Hirsch conjecture, which says that a stably parallelizable (closed) smooth $n$-manifold always embeds in $\Bbb R^{[(3/2)n]}$ (approximately). The conjecture has been verified when $M$ is $[n/4]$-connected.

A compact Lie group is parallelizable so, if the conjecture is true, then the top cell will split off after approximately $[n/2]$-suspensions if the Lie group has dimension $n$.