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

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

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 / 99 04 03 1 v 1 [ m at h . G T ] 8 A pr 1 99 9 INVARIANTS OF GENERIC IMMERSIONS AND BERNOULLI NUMBERS

First order invariants of generic immersions of manifolds of dimension nm−1 into manifolds of dimension n(m+1)−1, m, n > 1 are constructed using the geometry of self-intersections. The range of one of these invariants is related to Bernoulli numbers. As by-products some geometrically defined invariants of regular homotopy are found.

ar X iv : m at h / 99 05 11 4 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 REMARKS ON THE INTERSECTION OF FILTERS

We will show that that the existence of an uncountable family of nonmeager filter whose intersection is meager is consistent with MA(Suslin).