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Homotopy classification of nanophrases with at most four letters

Tomonori Fukunaga (2011)

Fundamenta Mathematicae

We give a homotopy classification of nanophrases with at most four letters. It is an extension of the classification of nanophrases of length 2 with at most four letters, given by the author in a previous paper. As a corollary, we give a stable classification of ordered, pointed, oriented multi-component curves on surfaces with minimal crossing number less than or equal to 2 such that any equivalent curve has no simply closed curves in its components.

Homotopy Lie algebras and fundamental groups via deformation theory

Martin Markl, Stefan Papadima (1992)

Annales de l'institut Fourier

We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as π * Ω S (the homotopy Lie algebra) or gr * π 1 S (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.

Hyperbolic knots and cyclic branched covers.

Luisa Paoluzzi (2005)

Publicacions Matemàtiques

We collect several results on the determination of hyperbolic knots by means of their cyclic branched covers. We construct examples of knots having two common cyclic branched covers. Finally, we briefiy discuss the problem of determination of hyperbolic links.

Incompressibilité des feuilles de germes de feuilletages holomorphes singuliers

David Marín, Jean-François Mattei (2008)

Annales scientifiques de l'École Normale Supérieure

Nous considérons un germe de feuilletage holomorphe singulier non-dicritique ℱ défini sur une boule fermée 𝔹 ¯ ⊂ ℂ 2 , satisfaisant des hypothèses génériques, de courbe de séparatrice S . Nous démontrons l’existence d’un voisinage ouvert U de S dans 𝔹 ¯ tel que, pour toute feuille L de ℱ | ( U ∖ S ) , l’inclusion naturelle ı : L ↪ U ∖ S induit un monomorphisme ı * : π 1 ( L ) ↪ π 1 ( U ∖ S ) au niveau du groupe fondamental. Pour cela, nous introduisons la notion géométrique de « connexité feuilletée » avec laquelle nous réinterprétons la notion d’incompressibilité....

Intrinsic linking and knotting are arbitrarily complex

Erica Flapan, Blake Mellor, Ramin Naimi (2008)

Fundamenta Mathematicae

We show that, given any n and α, any embedding of any sufficiently large complete graph in ℝ³ contains an oriented link with components Q₁, ..., Qₙ such that for every i ≠ j, | l k ( Q i , Q j ) | ≥ α and | a ₂ ( Q i ) | ≥ α , where a ₂ ( Q i ) denotes the second coefficient of the Conway polynomial of Q i .

Currently displaying 221 – 240 of 643