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Lie group framing and framed bordism

  1. What is the definition of Lie group framing, in simple terms?

  2. Is the Lie group framing of spheres a particular type of Lie group framing? (How special is the Lie group framing of spheres differed from the generality of Lie group framing?)

  3. Examples of Lie group framing includes:

  • $\Omega_3^{fr}=\mathbf{Z}/{24}$ generated by a 3-sphere $S_3=SU(2)$ with the Lie group framing.

  • $\Omega_6^{fr}=\mathbf{Z}/{2}$ generated by $S_3 \times S_3$ with the Lie group framing.

How do we construct the explicit class of $\mathbf{Z}/{24}$ and $\mathbf{Z}/{2}$ class of Lie group framing above?

http://www.map.mpim-bonn.mpg.de/Framed_bordism

zeta
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  • 1
  • 7