On some spaces which are covered by a product space
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 Spaces which can be Partioned by the Rational Line.
On some ternary operations in knot theory
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 Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.
Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.
On spaces which have the shape of C. W. complexes
On spaces with periodic cohomology.
On sprays and connections
[For the entire collection see Zbl 0699.00032.] A connection structure (M,H) and a path structure (M,S) on the manifold M are called compatible, if locally where and express the semi-spray S and the connection map H, resp. In the linear case of H its geodesic spray S is quadratic: On the contrary, the homogeneity condition of S induces the relation for the compatible connection H, whence it follows not that H is linear, i.e. if a connection structure is compatible with a spray, then...
On stability of 3-manifolds
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)
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 Stable Parallelizability of Gk,n and Related Manifolds.
On sums of algebraic surfaces.
On surface braids of index four with at most two crossings
Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.
On symmetric group actions on spin 4-manifolds.
On symplectic cobordism of real projective plane.
This note answers a question of V. V. Vershinin concerning the properties of Buchstaber's elements Θ2i+1(2) in the symplectic cobordism ring of the real projective plane. It is motivated by Roush's famous result that the restriction of these elements to the projective line is trivial, and by the relationship with obstructions to multiplication in symplectic cobordism with singularities.
On symplectic fillings.
On tame embeddings of solenoids into 3-space
Solenoids are inverse limits of the circle, and the classical knot theory is the theory of tame embeddings of the circle into 3-space. We make a general study, including certain classification results, of tame embeddings of solenoids into 3-space, seen as the "inverse limits" of tame embeddings of the circle. Some applications in topology and in dynamics are discussed. In particular, there are tamely embedded solenoids Σ ⊂ ℝ³ which are strictly achiral. Since solenoids are non-planar,...
On tensor representations of knot algebras.
On the (-1)-curve conjecture of Friedmann and Morgan.
On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant