I need to proof that the self intersection mod 2 of the central curve in a Möbius band, i.e., $I_2(X,X)=1$.
What I think is that we can use the homotopy invariance of the intersection no. and deform $X$ to get $X'$ which transversally intersects $X$.
But I am not exactly sure how it will help us to prove what is desired .
Kindly help!!
thanks & regards in advance