Hi, I have really appreciated the help understanding homology over the last week or two. I have a couple more questions, 28 and 29 again from 2.2 in Hatcher;
For the first part of 28 need to use the M-V sequence to find the homology groups of the space obtained by attaching the boundary circle of a möbius strip to the torus along the circle . Then the second part is the same question but we glue the boundary of the strip to the subset
I know basically how the MV sequence works, but I am not confident in using it for these spaces, visualisation of which I am finding daunting, especially the part about the real projective planes.
Q29 is very similar. We need to find the homology groups of the surface obtained by gluing the interiors of two surfaces of genus g (ie the compact spaces bounded by such) along the boundary, Mg. Also we need to find the relative homology groups of (R,Mg) where R is the "interior" of Mg.
Still a bit lost on these so any tips or anything would be appreciated, thanks!