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The possibility of a finite-time topological reconnection in the expanding Hele-Shaw flow of immiscible fluids is numerically investigated. The initial conditions correspond to those of a zero-surface tension exact solution found by Howison that develops cusp singularities by interface overlapping and thus constitute a natural candidate for potential topological singularities in the presence of small surface tension. Using a spectrally accurate boundary integral method it is found that in thedoi:10.1088/1468-5248/3/1/037 fatcat:dayscnyusfcp7astbmjupthlxy