By Joan S. Birman, Jane Gilman, William W. Menasco, Xiao-Song Lin
There are many specialties in low-dimensional topology which can locate of their 'family tree' a typical ancestry within the concept of floor mappings. those comprise knot thought as studied by using braid representations and 3-manifolds as studied by using Heegaard splittings. The learn of the outside mapping type staff (the modular staff) is naturally a wealthy topic in its personal correct, with family to many alternative fields of arithmetic and theoretical physics. yet its such a lot direct and noteworthy manifestation is maybe within the sizeable quarter of low-dimensional topology. even though the scene of this sector has been replaced dramatically and skilled major enlargement because the unique e-book of Professor Joan Birman's seminal paintings, "Braids, hyperlinks, and Mapping type teams" (Princeton college Press), she introduced jointly mathematicians whose study span many specialities, all of universal lineage.The subject matters coated are really varied. but they mirror good the purpose and spirit of the convention in low-dimensional topology held in honor of Joan S.Birman's seventieth birthday at Columbia collage (New York, NY), which was once to discover how those quite a few specialties in low-dimensional topology have diverged long ago 20-25 years, in addition to to discover universal threads and capability destiny instructions of improvement.
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