I have a graded vector space $V$ such that $V=V^2\bigoplus V^3$, i.e $V^k=0\quad \forall k\neq2,3.$

Now I can't understand what is $\bigwedge V^{\leq 2}$.

Is it $\bigwedge V^{\leq 2}=\bigwedge^0 V^{\leq 2}\bigoplus \bigwedge^1 V^{\leq 2}\bigoplus...$ with $V^{\leq 2}=V^2$?

Also what is $(\bigwedge V^{\leq 2})^2$?


  • 2
    $\begingroup$ Whatever it is, it's horrible notation. Where does this come from? $\endgroup$ – Lord Shark the Unknown Jul 7 at 6:25
  • $\begingroup$ From the book Rational Homotopy Theory $\endgroup$ – sasho98 Jul 7 at 6:26
  • 1
    $\begingroup$ I don't know that book ... does it have authors? $\endgroup$ – Lord Shark the Unknown Jul 7 at 6:26
  • $\begingroup$ Felix-Halperin-Thomas $\endgroup$ – sasho98 Jul 7 at 6:28
  • $\begingroup$ Can someone provide a pdf of the book Exterior algebras:elementary tribute to Grassman's ideas $\endgroup$ – sasho98 Jul 8 at 9:18

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