75 citations · 554 across the 50 of their papers we have counts for
10 papers · 1 filter
Singular Seifert surfaces and Smale invariants for a family of 3-sphere immersions
Tobias Ekholm, Masamichi Takase
A self-transverse immersion of the 2-sphere into 4-space with algebraic number of self intersection points equal to -n induces an immersion of the circle bundle over the 2-sphere o…
Cobordisms of fold maps and maps with prescribed number of cusps
Tobias Ekholm, Andras Szucs, Tamas Terpai
A generic smooth map of a closed -manifold into -space has a finite number of cusps (-singularities). We determine the possible numbers of cusps of such maps.…
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…
Regular homotopy and total curvature
Tobias Ekholm
We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopie…
Framed holonomic knots
Tobias Ekholm, Maxime Wolff
A holonomic knot is a knot in 3-space which arises as the 2-jet extension of a smooth function on the circle. A holonomic knot associated to a generic function is naturally framed…
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…