This talk is based on the speakers paper math.GT/0003089 in http://xxx.lanl.gov/ Let S^3_i be a 3-sphere embedded in the 5-sphere S^5 (i=1,2). Let S^3_1 and S^3_2 intersect transversely. Then the intersection C of S^3_1 and S^3_2 is a disjoint collection of circles. Thus we obtain a pair of 1-links, C in S^3_i (i=1,2), and a pair of 3-knots, S^3_i in S^5 (i=1,2). Conversely let (L_1,L_2) be a pair of 1-links and (X_1,X_2) be a pair of 3-knots. It is natural to ask whether the pair of 1-links (L_1,L_2) is obtained as the intersection of the 3-knots X_1 and X_2 as above. We give a complete answer to this question. We ask a question to generalize this result. (Problem from section 1 of the above paper.) Two copies of this paper have been placed on the bookshelf in Rawles Hall 107, close to the picture of Einstein. I can be found in Rawles Hall 411 and frequently in the lounge, Rawles Hall 107. Please drop by if you would like to discuss this topic further.
