# computer junction number using differential kinds

Let $M$ be a 2n dimensional manifold, and also allow $A$ be a n - dimensional cycle on M. I intend to calculate the self - junction $(A.A)$ of A with itself. Allow $\eta_A$ be the kind in $H^n(M, \mathbb{R})$ offered by the Poincare duality isomorphism, i.e. $\int_B \eta_A=(A.B)$ for an n - cycle B. After that by the regulation that junction of cycles represents taking wedge item, we have $\int_M \eta_A \wedge \eta_B=(A.B)$. Taking A = B, given that $\eta_A \wedge \eta_A =0$, I get $(A.A)=0$, which I do not assume holds true. Where am I failing?

$\omega \wedge \eta = (-1)^{ab}\eta \wedge \omega$ where $a$ is the measurement of $\omega$ and also $b$ is the measurement of $\eta$.

So your "given that $\eta_A \wedge \eta_A=0$" comment is just real when $n$ is weird.

Related questions