This article gives a brief introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other

Any sphere S n admits a metric of constant sectional curvature. These canonical metrics are homogeneous and Einstein, that is the Ricci curvature is a constant multiple of the metric. The spheres S 4m+3, m> 1 are known to have another Sp(m + 1)-homogeneous Einstein metric discovered by Jensen [Jen73]. In addition,

We show that the tree-level part of a theory of finite type invariants of 3-manifolds (based on surgery on objects called claspers, Y-graphs or clovers) is essentially given by classical algebraic topology in terms of the Johnson homomorphism and Massey products, for arbitrary 3-manifolds. A key role of our proof is played by the notion of a homology cylinder, viewed as an enlargement of the mapping class group, and an apparently new Lie algebra of graphs colored by H1(Σ) of a closed surface Σ, closely related to deformation quantization on a surface [AMR1, AMR2, Ko3] as well as to a Lie algebra that encodes the symmetries of Massey products and the Johnson homomorphism. In addition, we give a realization theorem for Massey products and the Johnson homomorphism by homology cylinders.

This paper computes the following quadratic Witt groups: Ln(Z[t ±]), Ln(Z[D∞],w), and UNiln(Z; Z ± , Z ±). We show, for example, that L3(Z[t]) is an infinite direct sum of cyclic groups of orders 2 and 4. The techniques used are quadratic linking forms over Z[t] for n odd and Arf invariants for n even. 1 Introduction and Statement of Results In this paper we complete the computation of the Wall surgery obstruction groups for the infinite dihedral group, the L-theory of the polynomial ring Z[t], the L-theory of the Laurent polynomial ring Ln(Z[t, t −1]), with either the trivial involution or the involution t ↦ → −t, and the Cappell unitary

This review article has grown out of notes for the three lectures the second author presented during the XXIV-th Winter School of Geometry and Physics in Srni, Czech Republic, in January of 2004. Our purpose is twofold. We want give a brief introduction to some of the techniques we have developed over the last 5 years

Abstract: We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres Σ 2n+1 the moduli space of Sasakian structures has infinitely many positive components determined by inequivalent underlying contact structures. We also prove the existence of Sasakian metrics with positive Ricci curvature on each of the 2 2m distinct diffeomorphism types of homotopy real projective spaces RP 4m+1. Milnor’s discovery of exotic spheres [Mil1] presented Riemannian geometry with a very natural question. What kind of special metrics or, more generally, geometric structures can exist on exotic spheres? Perhaps the most intriguing example of such a question concerns the existence of metrics with positive sectional curvature. In 1974 Gromoll and

Abstract. In a recent article the first three authors proved that in dimension 4m + 1 all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also conjectured that all such homotopy spheres in dimension 4m − 1, m ≥ 2 admit Sasakian-Einstein metrics [BGK03], and proved this for the simplest case, namely dimension 7. In this paper we describe computer programs that show that this conjecture is also true for 11-spheres and 15-spheres. Moreover, a program is given that determines the partition of the 8610 deformation classes of Sasakian-Einstein metrics into the 28 distinct oriented diffomorphism types in dimension 7. 1.

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We show that any number of disjointly embedded 2–spheres in 4–space can be pulled apart by a link homotopy, ie, by a motion in which the 2–spheres stay disjoint but are allowed to self-intersect.

Abstract. Let N and P be smooth closed manifolds of dimensions n and p respectively. Given a Thom-Boardman symbol I, a smooth map f: N → P is called an Ω I-regular map if and only if the Thom-Boardman symbol of each singular point of f is not greater than I in the lexicographic order. We will represent the group of all cobordism classes of Ω I-regular maps of n-dimensional closed manifolds into P in terms of certain stable homotopy groups. As an application we will study the relationship among the stable homotopy groups of spheres, the above cobordism group and higher singularities. 1.