Braids: A Survey

Joan Birman and Tara Brendle provide an interesting overview of a fascinating topic. A certain personal characteristic of both authors is worth noting in light of the recent Summers flap; it's surprising the number of women I personally know of doing research in geometry and related areas, given the "innate" limitations of their gender ...

This article is about Artin's braid group and its role in knot theory. We set ourselves two goals: (i) to provide enough of the essential background so that our review would be accessible to graduate students, and (ii) to focus on those parts of the subject in which major progress was made, or interesting new proofs of known results were discovered, during the past 20 years. A central theme that we try to develop is to show ways in which structure first discovered in the braid groups generalizes to structure in Garside groups, Artin groups and surface mapping class groups. However, the literature is extensive, and for reasons of space our coverage necessarily omits many very interesting developments. Open problems are noted and so-labelled, as we encounter them.

Comments

[Jim]

Among high school math teachers the conventional wisdom is that boys tend to do better at geometry, girls at algebra. Maybe it just has to do with males slightly better ability with spatial thinking. But then here you have this article showing that women are very active inb this area of geometry.

[Alek]

Subjects like algebraic geometry require very little spatial thinking.

[Abiola Lapite]

"Subjects like algebraic geometry require very little spatial thinking."

Perhaps - I think you might want to take a look at Shafarevich's textbook before pronouncing too definitely, as you might be surprised - but differential topology does.

[Peter Woit]

Hi Abiola,

I've never noticed seen evidence of women mathematicians having a preference for algebra over geometry. If anything, the opposite.

Joan Birman (note spelling!) has had a remarkable career. She's now 77 but still very active in mathematical research at a high level, something I think very few men have accomplished. While she's still active as a researcher, she very recently finally officially retired, there will be a conference in her honor in a couple weeks here at Columbia. She didn't actually get her Ph.D until she was 41. I guess this was because she mostly raised her children before seriously starting her research career.

[Abiola Lapite]

"note spelling!"

Thanks for pointing that out; it's fixed now. Birman's story is truly inspiring, especially in light of the widely-held conviction that mathematics is a young man's game.