Results 1  10
of
84
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 22 (3 self)
 Add to MetaCart
(Show Context)
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
Controlled Surgery with Trivial Local Fundamental Groups
 i1>NP1+>NP3+ ) ( \ /` \, ) ( X bias>NP5>o ) ( / \, /` ) ( i2>NP2+>NP4
, 2001
"... We provide a proof of the controlled surgery sequence, including stability, in the special case that the local fundamental groups are trivial. Stability is a key ingredient in the construction of exotic homology manifolds by Bryant, Ferry, Mio and Weinberger, but no proof has been available. The ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
(Show Context)
We provide a proof of the controlled surgery sequence, including stability, in the special case that the local fundamental groups are trivial. Stability is a key ingredient in the construction of exotic homology manifolds by Bryant, Ferry, Mio and Weinberger, but no proof has been available. The development given here is based on work of M. Yamasaki.
Triangular Witt Groups  Part I: The 12Term Localization Exact Sequence.
, 1999
"... . To a short exact sequence of triangulated categories with duality, we associate a long exact sequence of Witt groups. For this, we introduce higher Witt groups in a very algebraic and explicit way. Since those Witt groups are 4periodic, this long exact sequence reduces to a cyclic 12term one. Of ..."
Abstract

Cited by 17 (9 self)
 Add to MetaCart
(Show Context)
. To a short exact sequence of triangulated categories with duality, we associate a long exact sequence of Witt groups. For this, we introduce higher Witt groups in a very algebraic and explicit way. Since those Witt groups are 4periodic, this long exact sequence reduces to a cyclic 12term one. Of course, in addition to higher Witt groups, we need to construct connecting homomorphisms, hereafter called residue homomorphisms. Introduction. The reader is expected to have some interest in the usual Witt group, as defined for schemes by Knebusch in [9, definition p. 133]. This Witt group is obtained by considering symmetric vector bundles (up to isometry) modulo the bundles possessing a lagrangian  that is a maximal totally isotropic subbundle. This being said, the present article is maybe more about triangulated categories than about symmetric forms and that might possibly make it generalizable to invariants other than the Witt group. For the time being, it is not my goal to compute an...
the K andLtheory of the algebra of operators affiliated to a finite von Neumann algebra.” KTheory 24
, 2001
"... Abstract. We construct a real valued dimension for arbitrary modules over the algebra of operators affiliated to a finite von Neumann algebra. Moreover we determine the algebraic K0 and K1group and the Lgroups of such an algebra. 1. ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
Abstract. We construct a real valued dimension for arbitrary modules over the algebra of operators affiliated to a finite von Neumann algebra. Moreover we determine the algebraic K0 and K1group and the Lgroups of such an algebra. 1.
Surgery and the generalized Kervaire invariant
 Universitdt Bielefeld
, 1985
"... framed manifolds of dimension 4k+ 2 (see [12]) was an important stimulant for the development of surgery theory; but it also led to the theory of the 'generalized Kervaire Invariant ' of Browder and Brown [2, 3]. ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
(Show Context)
framed manifolds of dimension 4k+ 2 (see [12]) was an important stimulant for the development of surgery theory; but it also led to the theory of the 'generalized Kervaire Invariant ' of Browder and Brown [2, 3].
Triangular Witt Groups. Part II: From Usual To Derived
 Math. Z
, 1999
"... . We establish that the derived Witt group is isomorphic to the usual Witt group when 2 is invertible. This key result opens the Ali Baba's cave of triangular Witt groups, linking the abstract results of Part I to classical questions for the usual Witt group. For commercial purposes, we survey ..."
Abstract

Cited by 13 (8 self)
 Add to MetaCart
(Show Context)
. We establish that the derived Witt group is isomorphic to the usual Witt group when 2 is invertible. This key result opens the Ali Baba's cave of triangular Witt groups, linking the abstract results of Part I to classical questions for the usual Witt group. For commercial purposes, we survey the future applications of triangular Witt groups in the introduction. We also establish a connection between oddindexed Witt groups and formations. Finally, we prove that over a commutative local ring in which 2 is a unit, the shifted derived Witt groups are all zero but the usual one. Introduction The usual Witt group is the one defined by Knebusch (see [6]) for algebraic varieties. We present the obvious generalization of his definition to exact categories (see x 1) without any feeling of paternity. The derived Witt group is the Witt group of the derived category (see x 2), following the general definition for triangulated categories introduced in [1] and [2]. Let E be an exact category wit...
Generalized Arf invariants in algebraic Ltheory
"... Abstract. The difference between the quadratic Lgroups L∗(A) and the symmetric Lgroups L ∗ (A) of a ring with involution A is detected by generalized Arf invariants. The special case A = Z[x] gives a complete set of invariants for the Cappell UNilgroups UNil∗(Z; Z, Z) for the infinite dihedral gr ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
Abstract. The difference between the quadratic Lgroups L∗(A) and the symmetric Lgroups L ∗ (A) of a ring with involution A is detected by generalized Arf invariants. The special case A = Z[x] gives a complete set of invariants for the Cappell UNilgroups UNil∗(Z; Z, Z) for the infinite dihedral group D ∞ = Z2 ∗Z2, extending the results of Connolly and Ranicki [10], Connolly and Davis [8].