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Could you clarify what you mean by "braid link" and "proper link"? –  Ryan Budney Jan 29 '11 at 18:40
Oops! Alexander's Thm says that all tame links are closed braids, so "braid links"="tame links." I'm studying a result of Murakami in "A recursive calculation of the Arf invariant of a link" (J. Math. Soc. Japan 38, #2 (1986). Murakami says "a link $L$ is proper if $lk(K,L−K)$ is even for every component of $K$ in $L$, where $lk$ means a linking number," and I don't have a very good visual picture for what that means. In that sense, are most tame links proper? Few? –  tuppsphd Jan 30 '11 at 3:36
For a picture of what "linking number" means, see: en.wikipedia.org/wiki/Linking_number As Paul mentions, Murakami's notion of "proper link" is fairly special and most links aren't of that sort. Just so you know "proper link" isn't a standard terminology. –  Ryan Budney Jan 30 '11 at 6:40
According to the definitions in your comment, the closure of the 2 stranded braid with braid word $\sigma_1^6$ is not proper, since the closure is a 2 component link with linking number 3.