Twisted linking numbers via representations of fundamental groups

Using representations of fundamental groups, we introduce the concept of twisted linking numbers. If the corresponding representation is trivial, the twisted linking number coincides with the linking number. In the case of a nontrivial representation, however, this is not necessarily true, which implies that the twisted linking number can detect the nontriviality of an embedding of S 1 . An example is given for which the linking number is trivial but the twisted linking number is not.