7 citations · 13 across the 5 of their papers we have counts for
6 papers · 1 filter
Invariants of Knots, Embeddings and Immersions via Contact Geometry
Tobias Ekholm, John B. Etnyre
This paper is an overview of the idea of using contact geometry to construct invariants of immersions and embeddings. In particular, it discusses how to associate a contact manifol…
The complex shade of a real space and its applications
Tobias Ekholm
A natural oriented (2k+2)-chain in CP^{2k+1} with boundary twice RP^{2k+1}, its complex shade, is constructed. Via intersection numbers with the shade, a new invariant, the shade n…
Differential 3-knots in 5-space with and without self intersections
Tobias Ekholm
Regular homotopy classes of immersions of a 3-sphere in 5-space constitute an infinite cyclic group. The classes containing embeddings form a subgroup of index 24. The obstruction…
Geometric formulas for Smale invariants of codimension two immersions
Tobias Ekholm, Andras Szucs
We give three formulas expressing the Smale invariant of an immersion f of a (4k-1)-sphere into (4k+1)-space. The terms of the formulas are geometric characteristics of any generic…
Total curvatures of holonomic links
Tobias Ekholm, Ola Weistrand
A differential geometric characterization of the braid-index of a link is found. After multiplication by 2pi, it equals the infimum of the sum of total curvature and total absolute…
Invariants of generic immersions and Bernoulli numbers
Tobias Ekholm
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. Th…