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On the computation of the projective surgery obstruction groups
, 1993
"... The computation of the projective surgery obstruction groups LP.(ZG), for G a hyperelementary finite group, is reduced to standard calculations in number theory, mostly involving class groups. Both the exponent of the torsion subgroup and the precise divisibility of the signatures are determined. Fo ..."
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Cited by 5 (2 self)
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The computation of the projective surgery obstruction groups LP.(ZG), for G a hyperelementary finite group, is reduced to standard calculations in number theory, mostly involving class groups. Both the exponent of the torsion subgroup and the precise divisibility of the signatures are determined
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 ..."
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Cited by 23 (4 self)
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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
Mackey and Frobenius structures on odd dimensional surgery obstruction groups, KTheory 29
, 2003
"... Abstract. C. T. C. Wall formulated surgeryobstruction groups L n (Z[G]) in terms of quadratic modules and automorphisms. C. B. Thomas showed that the Wallgroup functors L n (Z [−], w − ) are modules over the Hermitianrepresentationring functor G 1 (Z, −) if the orientation homomorphism w is tr ..."
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Cited by 1 (0 self)
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Abstract. C. T. C. Wall formulated surgeryobstruction groups L n (Z[G]) in terms of quadratic modules and automorphisms. C. B. Thomas showed that the Wallgroup functors L n (Z [−], w − ) are modules over the Hermitianrepresentationring functor G 1 (Z, −) if the orientation homomorphism w
A holomorphic Casson invariant for CalabiYau 3folds, and bundles on K3 fibrations
 J. DIFFERENTIAL GEOM
, 2000
"... We briefly review the formal picture in which a CalabiYau nfold is the complex analogue of an oriented real nmanifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a holomorphic Casson invariant counting bundles on a CalabiYau 3fol ..."
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Cited by 199 (8 self)
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fold. We develop the deformation theory necessary to obtain the virtual moduli cycles of [LT], [BF] in moduli spaces of stable sheaves whose higher obstruction groups vanish. This gives, for instance, virtual moduli cycles in Hilbert schemes of curves in P 3, and Donaldson – and GromovWitten – like
The singularity obstruction for group splittings
 Topology Appl
"... We study an obstruction to splitting a finitely generated group G as an amalagamated free product or HNN extension over a given subgroup H and show that when the obstruction is “small ” G splits over a related subgroup. Applications are given which generalise decomposition theorems from low dimensio ..."
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Cited by 10 (1 self)
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We study an obstruction to splitting a finitely generated group G as an amalagamated free product or HNN extension over a given subgroup H and show that when the obstruction is “small ” G splits over a related subgroup. Applications are given which generalise decomposition theorems from low
GroupTheoretic Obstructions to Integrability
, 1995
"... Let V be a 4dimensional complex symplectic vector space. This paper classifies those connected linear algebraic subgroups of the symplectic group Sp(V ) that admit two independent rational invariants. As an application we show the nonintegrability of a three degree of freedom Hamiltonian syste ..."
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Cited by 1 (0 self)
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Let V be a 4dimensional complex symplectic vector space. This paper classifies those connected linear algebraic subgroups of the symplectic group Sp(V ) that admit two independent rational invariants. As an application we show the nonintegrability of a three degree of freedom Hamiltonian
Galoisian Obstructions to integrability of Hamiltonian Systems
, 2001
"... An inconvenience of all the known galoisian formulations of Ziglin’s nonintegrability theory is the Fuchsian condition at the singular points of the variational equations. We avoid this restriction. Moreover we prove that a necessary condition for meromorphic complete integrability (in Liouville se ..."
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Cited by 67 (11 self)
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sense) is that the identity component of the Galois group of the variational equation (in the complex domain) must be abelian. We test the efficacy of these new approaches on some examples. We will give some non academic applications in two following papers.
EQUIVARIANT SURGERY UNDER THE WEAK GAP CONDITION
"... Abstract. In this article we explain the equivariant surgery obstruction group with middle dimensional singular set and hypercomputability of this group. 1. ..."
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Abstract. In this article we explain the equivariant surgery obstruction group with middle dimensional singular set and hypercomputability of this group. 1.
Results 1  10
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2,948