On polynomial coverings and their classification.
Displaying 921 – 940 of 1631
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. positions of sets in spaces.
Karol Borsuk (1973)
Fundamenta Mathematicae
On real algebraic links in
R. Benedetti, M. Shiota (1998)
Bollettino dell'Unione Matematica Italiana
Viene presentata una costruzione che, dato un arbitrario nodo , produce allo stesso tempo: 1) un'applicazione polinomiale con singolarità (debolmente) isolata in e come tipo di nodo della singolarità; 2) una risoluzione delle singolarità di 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 Regular Coverings of Links.
Makoto Sakuma (1982)
Mathematische Annalen
On Regular Homotopy of Branched Coverings of the Sphere.
Ulrich Hirsch (1977)
Manuscripta mathematica
On Representing Homology Classes of 4-Manifolds.
Selman Akbulut (1978)
Inventiones mathematicae
On S-Equivalence of Seifert Matrices.
H.F. Trotter (1973)
Inventiones mathematicae
On signatures and a subgroup of a central extension to the mapping class group.
Natov, Jonathan (2003)
Homology, Homotopy and Applications
On signatures associated with ramified coverings and embedding problems
J. Wood, Emery Thomas (1973)
Annales de l'institut Fourier
Given a cohomology class there is a smooth submanifold Poincaré dual to . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in . This note summarizes some results on the question: how does the divisibility of restrict the dual submanifolds in this class ? A formula for signatures associated with a -fold ramified cover of branched along is given and a proof is included in case .
On singular cut-and-pastes in the 3-space with applications to link theory.
Fujitsugu Hosokawa, Shin'ichi Suzuki (1995)
Revista Matemática de la Universidad Complutense de Madrid
In the study of surfaces in 3-manifolds, the so-called ?cut-and-paste? of surfaces is frequently used. In this paper, we generalize this method, in a sense, to singular-surfaces, and as an application, we prove that two collections of singular-disks in the 3-space R3 which span the same trivial link are link-homotopic in the upper-half 4-space R3 [0,8) keeping the link fixed. Throughout the paper, we work in the piecewise linear category, consisting of simplicial complexes and piecewise linear maps....
On slice knots in the complex projective plane.
Akira Yasuhara (1992)
Revista Matemática de la Universidad Complutense de Madrid
We investigate the knots in the boundary of the punctured complex projective plane. Our result gives an affirmative answer to a question raised by Suzuki. As an application, we answer to a question by Mathieu.
On small geometric invariants of 3-manifolds.
Kapitza, Paul J. (2011)
The New York Journal of Mathematics [electronic only]
On some spaces which are covered by a product space
Izu Vaisman (1977)
Annales de l'institut Fourier
In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the...
On some ternary operations in knot theory
Maciej Niebrzydowski (2014)
Fundamenta Mathematicae
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, we obtain the relations from the knot group, and from the core group. Using the ternary operator approach, we generalize the Dehn presentation of the knot group to extra loops, and a similar presentation for the core group to the variety of Moufang loops.
On stability of 3-manifolds
Sławomir Kwasik, Witold Rosicki (2004)
Fundamenta Mathematicae
We address the following question: How different can closed, oriented 3-manifolds be if they become homeomorphic after taking a product with a sphere? For geometric 3-manifolds this paper provides a complete answer to this question. For possibly non-geometric 3-manifolds, we establish results which concern 3-manifolds with finite fundamental group (i.e., 3-dimensional fake spherical space forms) and compare these results with results involving fake spherical space forms of higher...
On stability of Alexander polynomials of knots and links (survey)
Mikami Hirasawa, Kunio Murasugi (2014)
Banach Center Publications
We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.
On symmetric group actions on spin 4-manifolds.
Liu, Ximin, Li, Hongxia (2007)
Acta Mathematica Universitatis Comenianae. New Series
On symplectic fillings.
Etnyre, John B. (2004)
Algebraic & Geometric Topology
On tensor representations of knot algebras.
Tammo tom Dieck (1997)
Manuscripta mathematica