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On framings of 3-manifolds. (English) Zbl 0716.57011
A 2-framing of a 3-manifold Y is a homotopy class of trivializations of the double \(2T_ Y=T_ Y\oplus T_ Y\) of its tangent bundle (as a Spin(6) bundle). This paper demonstrates the existence of canonical 2- framings for all oriented 3-manifolds and discusses their application in E. Witten’s extension of the Jones invariants to all 3-manifolds [Commun. Math. Phys. 121, 351-399 (1989; Zbl 0667.57005)] and in identifying certain central extensions of the mapping class group.
Reviewer: J.Hempel

57N10 Topology of general \(3\)-manifolds (MSC2010)
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
20E22 Extensions, wreath products, and other compositions of groups
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