منابع مشابه
Framed Knots in 3-manifolds
For a fixed isotopy type K of unframed knots in S there are infinitely many isotopy classes of framed knots that correspond to K when we forget the framing. We show that the same fact is true for all the isotopy types of unframed knots in a closed oriented 3-manifold M , provided that M 6= (S × S)#M . On the other hand for any M = (S × S)#M ′ we construct examples of isotopy classes of unframed...
متن کاملFramed Knots in 3-manifolds and Affine Self-linking Numbers
The number |K| of non-isotopic framed knots that correspond to a given unframed knot K ⊂ S is infinite. This follows from the existence of the self-linking number slk of a zerohomologous framed knot. We use the approach of Vassiliev-Goussarov invariants to construct “affine self-linking numbers” that are extensions of slk to the case of nonzerohomologous framed knots. As a corollary we get that...
متن کاملLefschetz fibrations, intersection numbers, and representations of the framed braid group
We examine the action of the fundamental group Γ of an mpunctured Riemann surface on the middle dimensional homology of a regular fiber in a Lefschetz fibration, and describe to what extent this action can be recovered from the intersection numbers of vanishing cycles. Basis changes for the vanishing cycles result in a nonlinear action of the framed braid group B̃ on m strings on a suitable spac...
متن کاملA FRAMED f(3, 1)− STRUCTURE ON TANGENT MANIFOLDS
A tangent manifold is a pair (M, J) with J a tangent structure (J2 = 0, ker J = im J) on the manifold M . A systematic study of tangent manifolds was done by I. Vaisman in [5]. One denotes by HM any complement of im J := TV . Using the projections h and v on the two terms in the decomposition TM = HM ⊕TV one naturally defines an almost complex structure F on M . Adding to the pair (M, J) a Riem...
متن کاملBraid structures in knot complements , handlebodies and 3 – manifolds Sofia
We consider braids on m + n strands, such that the first m strands are trivially fixed. We denote the set of all such braids by Bm,n. Via concatenation Bm,n acquires a group structure. The objective of this paper is to find a presentation for Bm,n using the structure of its corresponding pure braid subgroup, Pm,n, and the fact that it is a subgroup of the classical Artin group Bm+n. Then we giv...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1126197-1