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 the

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... se of an air bubble surface tension regularizes the cusped singularities and the solution clearly exist for all times forming the well known fingering and tip-splitting patterns. On the other hand, the presence of a viscous fluid in the interior of the bubble creates side-fingering and a complex evolution signalling finite-time topological reconfigurations of the fluid interface. With high resolution the collapsing exponent is obtained and it is found that the minimum distance between adjacent parts of the interface decreases linearly with time.