Algebraic Topology · Problem 2.1.6

Homology — Allen Hatcher

Mathematics — Topology · simplicial-homology-computations

Problem

Compute the simplicial homology groups of the

\Delta

-complex obtained from

n+1

2-simplices

\Delta^2_0, \cdots, \Delta^2_n

by identifying all three edges of

\Delta^2_0

to a single edge, and for

i > 0

identifying the edges

[v_0, v_1]

and

[v_1, v_2]

\Delta^2_i

to a single edge and the edge

[v_0, v_2]

to the edge

[v_0, v_1]

\Delta^2_{i-1}