m at h . G T ] 7 M ay 1 99 9 TOTAL CURVATURES OF HOLONOMIC LINKS

m at h . G T ] 1 9 M ay 1 99 9 TOTAL CURVATURES OF HOLONOMIC LINKS TOBIAS

A differential geometric characterization of the braid-index of a link is found. After multiplication by 2π, it equals the infimum of the sum of total curvature and total absolute torsion over holonomic representatives of the link. Upper and lower bounds for the infimum of total curvature over holonomic representatives of a link are given in terms of its braid-and bridge-index. Examples showing...

ar X iv : m at h / 99 05 00 1 v 1 [ m at h . A G ] 1 M ay 1 99 9 Tacnodes and cusps

ar X iv : m at h / 99 05 15 4 v 1 [ m at h . G T ] 2 5 M ay 1 99 9 SUBSPACES OF KNOT SPACES

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.

ar X iv : m at h / 98 12 07 1 v 2 [ m at h . G T ] 7 J an 1 99 9 HIGHER SKEIN MODULES

We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.

ar X iv : 0 70 5 . 41 66 v 1 [ m at h . G T ] 2 9 M ay 2 00 7 CLASSIFICATION OF FRAMED LINKS IN 3 - MANIFOLDS

We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: Theorem. Let M be a connected oriented closed smooth 3-manifold. Let L1(M) be the set of framed links in M up to a framed cobordism. Let deg : L1(M) → H1(M ;Z) be the map taking a framed link to its homology class. Then for each α ∈ H1(M ;Z) there is a 1-1 ...