I'm attempting to calculate the homology groups of this space and need some help.
Let $B$ be a 2-dimensional disk and $A$ a discrete set in its interior. Then let’s say we have a fiber bundle $X$ of a space (in this case a closed compact surface) over $B-A$. How would I go about calculating homology groups of the space $X$ where we identify all the holes in the bundle as one point? I wanted to use the face that it’s a fiber bundle, but at the point I quotient out it isn’t a bundle.
I’m also pretty new to algebraic topology generally. Any help is appreciated!