Math 535, Homework 2, due Nov 8
(1) Prove that if a lattice L has a (not necessarily maximal) chain
0 = m0 < m1 < < mk =
with each mi modular in L, then Hi (|L|) vanishes for i < k 2.
(2) Let G be a nite group, and S(G) be the subnormal subgroup
Math 535, Homework 1, due Oct 1
(1) If is a nite simplicial complex on vertex set V , and S V ,
then the induced subcomplex on S (denoted [S]) is the simplicial complex with all faces of that are contained in S.
Characterize the simplicial complexes such
Math 535, Homework 3, due Dec 16
(1) (a) Find a triangulation of the dunce cap.
(b) Find a partitioning of your triangulation, or show that it
is not partitionable.
(c) Calculate the f -vector and h-vector for your triangulation.
(2) For arbitrary k and n