An Example of "rubber sheet geometry."

The linked and unlinked two hole torus.

T1: An unlinked two hole torus .
T2: A linked two hole torus.

Fact: A. T1 and T2 are topologically equivalent by a cut and paste demonstration.

B. T1 and T2 are topologically equivalent by a homotopy equivalence. A rubber sheet transformation of T1 to T2 : H(t) for t in [0,1] in which at each stage H(t) is topologically equivalent to T1.