Assignment:
Qa) Show that the projective space with a disk removed (more precisely, the image of a disk on S2 under the natural projection pi : S2 -> P2 removed) is a M¨obius band.
Qb) Let M be the connected sum of two copies of the projective space formed by removing a disk from each copy of P2 and gluing the resulting surfaces together along the boundaries of the holes. Which standard surface do you obtain?
Please review the document enclosed here:
Attachment:- Ugly picture.rar
Provide complete and step by step solution for the question and show calculations and use formulas.