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On polynomials and surfaces of variously positive links

Alexander Stoimenow (2005)

Journal of the European Mathematical Society

It is known that the minimal degree of the Jones polynomial of a positive knot is equal to its genus, and the minimal coefficient is 1, with a similar relation for links. We extend this result to almost positive links and partly identify the next three coefficients for special types of positive links. We also give counterexamples to the Jones polynomial-ribbon genus conjectures for a quasipositive knot. Then we show that the Alexander polynomial completely detects the minimal genus and fiber property...

On pseudo-isotopy classes of homeomorphisms of a dimensional differentiable manifold.

Alberto Cavicchioli, Friedrich Hegenbarth (1998)

Revista Matemática Complutense

We study self-homotopy equivalences and diffeomorphisms of the (n+1)-dimensional manifold X= #p(S1 x Sn) for any n ≥ 3. Then we completely determine the group of pseudo-isotopy classes of homeomorphisms of X and extend to dimension n well-known theorems due to F. Laudenbach and V. Poenaru (1972,1973), and J. M. Montesinos (1979).

On real algebraic links in S 3

R. Benedetti, M. Shiota (1998)

Bollettino dell'Unione Matematica Italiana

Viene presentata una costruzione che, dato un arbitrario nodo L ⊆ S 3 , produce allo stesso tempo: 1) un'applicazione polinomiale f : R 4 , 0 → R 2 , 0 con singolarità (debolmente) isolata in 0 e L come tipo di nodo della singolarità; 2) una risoluzione delle singolarità di f nel senso di Hironaka. Specializzando la costruzione ai nodi fibrati otteniamo una versione debole (a meno di scoppiementi e nella categoria analitica reale) di un reciproco per il teorema di fibrazione di Milnor.

On real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

We prove that for any positive integers n 1 , n 2 , ... , n k there exists a real flag manifold F ( 1 , ... , 1 , n 1 , n 2 , ... , n k ) with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.

On residue formulas for characteristic numbers

Francisco Gómez Ruiz (2009)

Banach Center Publications

We show that coefficients of residue formulas for characteristic numbers associated to a smooth toral action on a manifold can be taken in a quotient field Q ( X ₁ , . . . , X r ) . This yields canonical identities over the integers and, reducing modulo two, residue formulas for Stiefel Whitney numbers.

On riemannian foliations with minimal leaves

Jesús A. Alvarez Lopez (1990)

Annales de l'institut Fourier

For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is ≤ 2 , a simple characterization of this geometrical property is proved.

On second order Thom-Boardman singularities

László M. Fehér, Balázs Kőműves (2006)

Fundamenta Mathematicae

We derive closed formulas for the Thom polynomials of two families of second order Thom-Boardman singularities Σ i , j . The formulas are given as linear combinations of Schur polynomials, and all coefficients are nonnegative.

Currently displaying 221 – 240 of 575