Results 1 to 10 of about 1,087,957 (214)
Regular homotopy classes of singular maps [PDF]
Proceedings of the London Mathematical Society, 2005 Two locally generic maps f,g : M^n --> R^{2n-1} are regularly homotopic if they lie in the same path-component of the space of locally generic maps. Our main result is that if n is not 3 and M^n is a closed n-manifold then the regular homotopy class of ...
Juhasz, Andras
core +6 more sources
Regular homotopy and total curvature [PDF]
Algebraic & Geometric Topology, 2006 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 homotopies, its infima in regular homotopy classes, and the homotopy types of ...
Ekholm, Tobias
core +11 more sources
Regular homotopy of Hurwitz curves [PDF]
Izvestiya: Mathematics, 2004 We prove that any two irreducible cuspidal Hurwitz curves $C_0$ and $C_1$ (or more generally, curves with A-type singularities) in the Hirzebruch surface $F_N$ with coinciding homology classes and sets of singularities are regular homotopic; and ...
Auroux, Denis +2 more
core +7 more sources
Homotopy invariance of tame homotopy groups of regular schemes [PDF]
manuscripta mathematica, 2021 The étale homotopy groups of schemes as defined by Artin and Mazur [1] have the disadvantage of being homotopy invariant only in characteristic zero. This and other related problems led to the definition of the tame topology which is coarser than the ...
A. Schmidt
semanticscholar +5 more sources
Regular homotopy classes of locally generic mappings [PDF]
Topology and its Applications, 2004 14 pages, 5 ...
A. Juhász
semanticscholar +6 more sources
Bordism and regular homotopy of low-dimensional immersions [PDF]
Pacific Journal of Mathematics, 1992 To obtain explicit generators for the groups of regular homotopy classes of immersions of the \(k\)-sphere in \(\mathbb{R}^ n\), the author defines an immersion invariant as an element of the \(k\)-th homotopy group of a Stiefel manifold. Using this invariant, he obtains generators for some groups of low-dimensional immersions.
J. Hughes
semanticscholar +4 more sources
The homotopy sequence for regular singular stratified bundles [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2016 A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber.
G. Battiston, L. Kindler
semanticscholar +6 more sources
Entropy, 2023 Universal Causality is a mathematical framework based on higher-order category theory, which generalizes previous approaches based on directed graphs and regular categories.
Sridhar Mahadevan
doaj +2 more sources
Tight surfaces and regular homotopy
Topology, 1986 Smooth immersions \(f: M^ 2\to E^ 3\) with \(\int_{M}| K| =2\pi (4-\chi (M))\) (tight immersions) are known to exist for all closed surfaces \(M^ 2\) except for the Klein bottle, the projective plane and the surface with \(\chi =-1\) (unknown case). All these examples lie in the standard regular homotopy class of immersions, and in 1960 N. H.
U. Pinkall
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Regular homotopy classes of immersed surfaces
Topology, 1985 There are two relevant equivalence relations on the set of immersions from a manifold \(M^ m\) into Euclidean space \({\mathbb{R}}^ n:\) regular homotopy and a second coming from the action of diffeomorphisms of M on it. Imposing both relations defines the term ''immersed manifold''.
U. Pinkall
semanticscholar +3 more sources