Combinatorial Topology
In
mathematics
,
combinatorial topology
was an older name for
algebraic topology
, dating from the time when
topological invariants
of spaces (for example the
Betti numbers
) were regarded as derived from combinatorial decompositions such as
simplicial complexes
. After the proof of the
simplicial approximation theorem
this approach provided rigour. The change of name, probably in the
1930s
, reflected the move to organise topological classes such as cycles
modulo
boundaries explicitly into
abelian groups
. This point of view is often attributed to
Emmy Noether
, and so the change of title may reflect her influence.
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