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Fundamental group
In the
mathematics
of
algebraic topology
, the
fundamental group
is a
mathematical group
associated to any given
pointed topological space
that provides a way to determine when two
path
s, starting and ending at a fixed
base point
, can be continuously deformed into each other. It records information about the basic shape, or holes, of the
topological space
. The fundamental group is the first and simplest
homotopy group
. The fundamental group is a
topological invariant
:
homeomorphic
topological spaces have the same fundamental group.
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