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We construct infinite families of topologically isotopic, but smoothly distinct knotted spheres, in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with S 2 ×S 2 , and as a consequence, analogous families of diffeomorphisms and metrics of positive scalar curvature for such 4-manifolds. We also construct… (More)

There is great value in employing the collective problem-solving power of large groups of people. Technological advances have allowed computer games to be utilized by a diverse population to solve problems. Science games are becoming more popular and cover various areas such as sequence alignments, DNA base-pairing, and protein and RNA folding. While these… (More)

Some of the party games that young teenagers play have surprisingly rich mathematical content. " Entanglement " is one such game in which couples are linked with strings tied tightly to their wrists, as shown in Figure 1(a) (a) (b) Figure 1: Entanglement and then challenged to disentangle themselves, often leading to Figure 1(b). In fact there is a quick… (More)

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