/sci/ - Science & Math

>>9515187
Ok I know there some topologists in here.

How tf do I do this?

"5. Consider the space Y from HW 1.

a) Show that the 0-cell has an open neighborhood C homeomorphic to the cone on a torus. Hint: The preimage of C in the two simplices before identifications is a disjoint union of 8 cones, each being a cone on a triangle. By inspection (or by an Euler characteristic argument), the 8 triangles glue together to form a torus.

b) Let M=Y-C. Show that M is an orientable manifold with boundary a torus.

c) By the "half lives, half dies" theorem the kernel K of H_1(bd M)-> H_1(M) has rank 1. Draw a curve in Y generating K. Hint: Note that M/bd M is homeomorphic to Y."

(This was HW that was due today, so not cheating.)