|YURIY SHKOLNIKOV, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada|
|A generalisation of Whitney's trick in dimension 4, borromeanism and related questions|
It is well known that the classical Whitney's trick for 2-submanifolds X and Y of a 1-connected PL (or smooth) 4-manifold M does not work. It has not been noticed that the obstruction to it lies in the topology of Borromean-like links in S3. This gives a rise to an idea of simultaneous performing of the Whitney-like trick with 2 or more Whitney pairs of intersection points of X and Y. Under certain conditions such a trick (called a Whitney's multitrick) turns out to be successful. The distinctive feature of a multitrick is that it can be performed only collectively which means that for each separate pair of Whitney's points the classical trick does not work.