MATH 7520: Algebraic Topology Homework
MATH 7520 Algebraic Topology
- Show that a Δ-complex is a CW-complex.
- If X is the torus, the real projective plane, the Klein bottle, your favorite other surface, exhibit a Δ-complex structure on X, and use it to compute the simplicial homology of X.
- Problem #8 from §2.1 in Hatcher
- Problem #23 from §2.1 in Hatcher
- Problems #11 - 13 from §2.1 in Hatcher
- Problems #16, 17, 20, 22 from §2.1 in Hatcher
- Compute the local homology groups H*(CT,CT-x), where T is the 2-dimensional torus, CT is the cone on T, and x is the cone point.
- Look at problems #1 - 8 from §2.2 in Hatcher
- Compute H*( RPn ; Z/k ).
- Compute the homology and cohomology of the configuration space of 3 ordered points in the plane.
- Problems #6, 8, 9 from §3.1 in Hatcher
- Determine the structure of the cohomology rings H*( RP3 ; Z/2 ) and H*( K ; Z/2 ), where K is the Klein bottle.
- Problem #1 from §3.2 in Hatcher
to MATH 7520;
to my homepage.