The rank of the
-dimensional
Betti group
with integral coefficients. For each
the Betti number
is a topological invariant of the polyhedron which realizes the complex
,
and it indicates the number of pairwise
non-homological (over the rational numbers) cycles in it. For instance, for the sphere
:
for the projective plane
:
for the torus
:
For an
-dimensional
complex
the sum
is equal to its
Euler characteristic.
Betti numbers were introduced by
E. Betti
[1].