I am trying to figure out the $CW$ complex structure on a sphere with the north and south pole identified. I've been told the structure is the following
Start with a $0$-cell $x$.
Attach an oriented $1$-cell $e$ with both endpoints identified to $x$.
Attach a $2$-cell $σ$ with attaching map defined on its oriented boundary circle $∂σ$ as follows:
Subdivide $∂σ$ as a concatenation of two arcs $∂σ=∂1σ∗∂2σ$,
Map $∂1σ$ to $e$,
Map $∂2σ$ to $e¯$.
The problem is that I don't understand why or if this is indeed the $CW$ structure. First of all I don't know what $e¯$ means. I assume is the inverse of $e$. So does the above say we attach the half circle of the boundary of our disk to the oriented circle (of the 1 skeleton) and then the second half but in opposite orientation?. I don't understand how this attachment is possible. I don't even know what happens in the simple scenario of say we want to attach the circular part of the boundary of a half disk to a circle? This really confuses me... how can we attach something smaller to something bigger?
Can anyone explain me whats going on here
Thanks in advance