Some intricate noninvertible links

Wilbur Whitten
1970 Bulletin of the American Mathematical Society  
Let L be an oriented, ordered link imbedded in the oriented 3sphere S 3 , and let fx and K be integers such that 1 S^K<JX. We say that L is a generalized noninvertible link for the pair ju, K (or a (ju, K)I link) if it satisfies : (i) L has ix components ; (ii) Each sublink with K or fewer components is invertible ; (iii) Each sublink with more than K components is noninvertible, L is invertible provided it is of the same (oriented) type as its inverse. The inverse of L is obtained by reversing
more » ... tained by reversing the orientation of each component of L. Now (2, 1)1 links were exhibited in [2] and a (jtx, ju~ 1)1 link was given in [3] for each juâ3. In this announcement we outline the construction of a generalized noninvertible link for each pair ju, K such that 1 ^K <ju and ju è 3. Details will appear elsewhere.
doi:10.1090/s0002-9904-1970-12578-2 fatcat:jk5qha2zwrdebnwcsnoujj4xk4