The generators of $Omega_10^Pin^-(pt)=mathbbZ_128 times mathbbZ_8 times mathbbZ_2$

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From the literature I learned that the Pin$^-$ bordism group of a point in 10 dimensions is:

$$Omega_10^Pin^-(pt)=mathbbZ_128 times mathbbZ_8 times mathbbZ_2$$



  • What are their 10-dimension manifold generators?


  • What are their topological invariants (characteristic classes, or manifold signatures, or Dirac operators, eta or ABK invariants) can distinguish all $mathbbZ_128 times mathbbZ_8 times mathbbZ_2$ classes?




differential-geometry algebraic-topology differential-topology geometric-topology cobordism




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    From the literature I learned that the Pin$^-$ bordism group of a point in 10 dimensions is:

    $$Omega_10^Pin^-(pt)=mathbbZ_128 times mathbbZ_8 times mathbbZ_2$$



    • What are their 10-dimension manifold generators?


    • What are their topological invariants (characteristic classes, or manifold signatures, or Dirac operators, eta or ABK invariants) can distinguish all $mathbbZ_128 times mathbbZ_8 times mathbbZ_2$ classes?




    differential-geometry algebraic-topology differential-topology geometric-topology cobordism




    share|cite|improve this question





















      up vote
      1
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      favorite
      2









      up vote
      1
      down vote

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      2






      2





      From the literature I learned that the Pin$^-$ bordism group of a point in 10 dimensions is:

      $$Omega_10^Pin^-(pt)=mathbbZ_128 times mathbbZ_8 times mathbbZ_2$$



      • What are their 10-dimension manifold generators?


      • What are their topological invariants (characteristic classes, or manifold signatures, or Dirac operators, eta or ABK invariants) can distinguish all $mathbbZ_128 times mathbbZ_8 times mathbbZ_2$ classes?




      differential-geometry algebraic-topology differential-topology geometric-topology cobordism




      share|cite|improve this question











      From the literature I learned that the Pin$^-$ bordism group of a point in 10 dimensions is:

      $$Omega_10^Pin^-(pt)=mathbbZ_128 times mathbbZ_8 times mathbbZ_2$$



      • What are their 10-dimension manifold generators?


      • What are their topological invariants (characteristic classes, or manifold signatures, or Dirac operators, eta or ABK invariants) can distinguish all $mathbbZ_128 times mathbbZ_8 times mathbbZ_2$ classes?





      differential-geometry algebraic-topology differential-topology geometric-topology cobordism





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      asked Jul 21 at 2:12









      wonderich

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