Showing papers in "Topology in 2001"

TL;DR: In this paper, it was shown that for any splitting of a 3-manifold which is Seifert fibered or contains an essential torus, the subcomplexes are at most two apart in the simplicial distance on the curve complex.

TL;DR: In this article, it was shown that the coefficients of the Taylor expansion at q = 1 are equal to the numbers ξD of regular linearized chord diagrams as defined by Stoimenow and hence give an upper bound for the number of linearly independent Vassiliev invariants of degree D. The same values and derivatives of all orders at all roots of unity are obtained as the limiting value of the function − 1 2 ∑ n∈ Z (−1) n |6n+1|q (3n 2 +n)/2, the "der

TL;DR: In this article, the Landweber-Araki theory of Real cobordism and Real-oriented spectra is used to define a real analogue of the Adams-Novikov spectral sequence.

TL;DR: In this paper, the singular cochain functor with coefficients in F p induces a contravariant equivalence between the homotopy category of connected p-complete nilpotent spaces of finite p-type and a full subcategory of E ∞ F p -algebras.

TL;DR: In this article, a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1 is given, considering Dehn twists on a very simple set of curves.

TL;DR: In this article, the moduli spaces of representations of the fundamental group of a surface of genus g > 2 in the Lie groups SU(2,2) and Sp(4, R) were studied.

TL;DR: In this paper, a version of the Atiyah-Segal completion theorem for proper actions of an infinite discrete group G-CW-complex X has been proved for any finite proper CW complex X, and it has been shown that KG(X) is the Grothendieck group of the monoid of G-vector bundles over X.

TL;DR: In this article, it was shown that the stable homotopy of an algebraic theory is determined by a ring spectrum functorially associated with the theory, and that the theory is isomorphic to the topological Hochschild homology of the parameterizing ring spectrum.

TL;DR: In this article, a geometric slice-like characterization for the vanishing of Milnor's link invariants was given by proving the k-slice conjecture, which states that a link has vanishing Milnor -invariants of length 2k if and only if bounds disjoint surfaces in a four disk in such a way that the fundamental group of the complement admits free nilpotent quotients of class k.

TL;DR: In this paper, the authors consider a generalization of manifolds and orbifolds called quasifolds, which are locally isomorphic to the quotient of the space R k by the action of a discrete group, typically they are not Hausdorff topological spaces.

TL;DR: In this paper, it was shown that for a triangulated category T =D(R) of rings, there exists a homological functor which is not a restriction of representable functors.

TL;DR: In this article, the accessibility property of partially hyperbolic diffeomorphisms was studied in the context of a neighborhood of a topologically transitive (respectively volume preserving) Anosov flow.

TL;DR: In this paper, it was shown that a minimal surface of general type with p g (S ) = 0 and K s 2 ⩾3 for which the bicanonical map ϕ : S→ P K_S 2 is a morphism is a Burniat surface.

TL;DR: In this article, it was shown that if two Zariski dense representations, from a group G into Iso(X) where X is a rank one symmetric space, have the proportional marked length spectrum, then they are conjugate.

TL;DR: In this paper, an invariant of closed 3-manifolds counting the signed equivalence classes of representations of the fundamental group in SL 2 (C ) was defined, which is an analog of the Casson-Walker invariant for SU(2).

TL;DR: In this article, a 16-vertex K3 surface is shown to be invariant under the group AGL(1, F 16 )≅ F 4 ⊕2 ⋊ C 15 of order 240 acting transitively on the set of oriented edges.

TL;DR: In this article, it was shown that every connected CW-complex is the quotient of a contractible complex by a proper action of a discrete group, and that every CW-completeness of an aspherical complex can be computed by a group of order two, up to homotopy equivalence.

TL;DR: For any surface of genus at aleast 3 and a subgroup of finite index containing the Torellli group, the first cohomology group of any subgroup in a surface mapping class group must be trivial.

TL;DR: This article corrected errors in Hatcher and Oertel's table of boundary slopes of Montesinos knots which have projections with 10 or fewer crossings and showed that the table is correct.

TL;DR: In this paper, the obstruction for a generic immersion to be regularly homotopic to an embedding is described in terms of geometric invariants of its self-intersection, which are analogous to Arnold's invariants on plane curves.

TL;DR: In this article, it was shown that the p-adic valuation of the quantum SO(3)-invariant of a 3-manifold M, for odd primes p, is bounded below by a linear function of the mod p first betti number of M.

TL;DR: In this article, the authors used the discrete Morse theory of R. Forman to find a basis for the unique nonzero homology group of the complex of 2-connected graphs on n vertices.

TL;DR: In this article, a topological symmetric spectrum in the sense of Hovey et al. (Symmetric Spectra, preprint, 1998) was constructed, which represents (periodic) topological real K-theory.

TL;DR: The rational homology of the Torelli group of genus g relative to n distinguished points and r fixed embedded disks was shown to be infinite dimensional when g is sufficiently large as mentioned in this paper.

TL;DR: In this article, an analog of the Lusternik-Schnirelman theory for closed 1-forms is proposed, where cup-products and higher Massey products are used to find topological lower bounds on the minimal number of geometrically distinct critical points of any closed form in a given cohomology class.