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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

##### MSC:
 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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