Results 1  10
of
107
The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine 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 ..."
Abstract

Cited by 631 (15 self)
 Add to MetaCart
This article gives a brief introduction to the OnLine 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
Einstein metrics on spheres
 Ann. of Math
, 2005
"... 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 ..."
Abstract

Cited by 18 (13 self)
 Add to MetaCart
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,
Tree level invariants of threemanifolds, massey products and the Johnson homomorphism
, 1999
"... We show that the treelevel part of a theory of finite type invariants of 3manifolds (based on surgery on objects called claspers, Ygraphs or clovers) is essentially given by classical algebraic topology in terms of the Johnson homomorphism and Massey products, for arbitrary 3manifolds. A key r ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
We show that the treelevel part of a theory of finite type invariants of 3manifolds (based on surgery on objects called claspers, Ygraphs or clovers) is essentially given by classical algebraic topology in terms of the Johnson homomorphism and Massey products, for arbitrary 3manifolds. 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.
The surgery obstruction groups of the infinite dihedral group
 Geometry and Topology
"... 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 ev ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
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 Ltheory of the polynomial ring Z[t], the Ltheory of the Laurent polynomial ring Ln(Z[t, t −1]), with either the trivial involution or the involution t ↦ → −t, and the Cappell unitary
Sasakian geometry, hypersurface singularities, and Einstein
, 2005
"... This review article has grown out of notes for the three lectures the second author presented during the XXIVth 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 ov ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
This review article has grown out of notes for the three lectures the second author presented during the XXIVth 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
Sasakian geometry, homotopy spheres and positive Ricci curvature
, 2002
"... 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 hom ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
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.
Cobordism of maps without prescribed singularities
"... Abstract. Let N and P be smooth closed manifolds of dimensions n and p respectively. Given a ThomBoardman symbol I, a smooth map f: N → P is called an Ω Iregular map if and only if the ThomBoardman symbol of each singular point of f is not greater than I in the lexicographic order. We will repres ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Abstract. Let N and P be smooth closed manifolds of dimensions n and p respectively. Given a ThomBoardman symbol I, a smooth map f: N → P is called an Ω Iregular map if and only if the ThomBoardman 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 Iregular maps of ndimensional 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.
Einstein metrics on exotic spheres in dimensions 7
"... 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 SasakianEinstein. They also conjectured that all such homotopy spheres in dimension ..."
Abstract

Cited by 9 (7 self)
 Add to MetaCart
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 SasakianEinstein. They also conjectured that all such homotopy spheres in dimension 4m − 1, m ≥ 2 admit SasakianEinstein 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 11spheres and 15spheres. Moreover, a program is given that determines the partition of the 8610 deformation classes of SasakianEinstein metrics into the 28 distinct oriented diffomorphism types in dimension 7. 1.
Exotic spheres with positive Ricci curvature
 MR 98i:53058
, 1997
"... We show that a certain class of manifolds admit metrics of positive Ricci curvature. This class includes many exotic spheres, including all homotopy spheres which represent elements of bP2n. x0. In this paper we investigate the Ricci curvature of a certain class of manifolds which includes many exot ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
We show that a certain class of manifolds admit metrics of positive Ricci curvature. This class includes many exotic spheres, including all homotopy spheres which represent elements of bP2n. x0. In this paper we investigate the Ricci curvature of a certain class of manifolds which includes many exotic spheres. In particular we will be concerned with constructing metrics of positive Ricci curvature. Our main result is as follows: Theorem 2.1. Homotopy spheres which bound parallelisable manifolds admit metrics of positive Ricci curvature. The di eomorphism classes of homotopy spheres bounding parallelisable manifolds of dimension m form an abelian group under the connected sum operation. This group is denoted bPm. It was shown by Kervaire and Milnor in [5] that bPodd =0,bP4k+2 is either 0 or Z2