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737,278
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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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
The homogeneous coordinate ring of a toric variety
, 1992
"... This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X) of ..."
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Cited by 474 (7 self)
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be constructed as the quotient (C n+1 −{0})/C ∗. In §2, we will see that there is a similar construction for any toric variety X. In this case, the algebraic group G = HomZ(An−1(X), C ∗ ) acts on an affine space C ∆(1) such that the categorical quotient (C ∆(1) − Z)/G exists and is isomorphic to X
Integral representations of the infinite dihedral group
"... We want to study the representations of the infinite dihedral group D ∞ in GL2(R), where R is either the valuation ring Z(p) of rational numbers with denominator prime to p or the ring of padic integers Zp for some prime p. The motivation for this research comes from the homotopy theory of classify ..."
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Cited by 1 (1 self)
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We want to study the representations of the infinite dihedral group D ∞ in GL2(R), where R is either the valuation ring Z(p) of rational numbers with denominator prime to p or the ring of padic integers Zp for some prime p. The motivation for this research comes from the homotopy theory
Algebraic Ktheory over the infinite dihedral group
, 2008
"... A group G with an epimorphism G → D ∞ onto the infinite dihedral group D ∞ = Z2 ∗ Z2 = Z ⋊ Z2 inherits an amalgamated free product structure G = G1 ∗F G2 with F an index 2 subgroup of G1 and G2. Also, there is an index 2 subgroup ¯ G ⊂ G with an HNN structure ¯ G = F ⋊α Z. For such a G we obtain ..."
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Cited by 21 (4 self)
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A group G with an epimorphism G → D ∞ onto the infinite dihedral group D ∞ = Z2 ∗ Z2 = Z ⋊ Z2 inherits an amalgamated free product structure G = G1 ∗F G2 with F an index 2 subgroup of G1 and G2. Also, there is an index 2 subgroup ¯ G ⊂ G with an HNN structure ¯ G = F ⋊α Z. For such a G we obtain
1ALGEBRAIC KTHEORY OVER THE INFINITE DIHEDRAL GROUP
, 2008
"... the homotopy groups of a spectrum K (E) (Quillen, 1972). I K0(E) = class group of E, with one generator [P] for each object P in E, and one relation [P] − [Q] + [R] = 0 for each exact sequence in E 0 → P → Q → R → 0. I K1(E) = torsion group of E, with one generator τ(f) for each automorphism f: P ..."
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extensions K∗(R[t]) = K∗(R) ⊕ Ñil∗−1(R), K∗(R[t, t−1]) = K∗(R) ⊕ K∗−1(R) ⊕ Ñil∗−1(R) ⊕ Ñil∗−1(R) have been recently extended to a splitting theorem for the algebraic Ktheory of a dihedral extension K∗(R[D∞]) = K∗(R → R[Z2] × R[Z2]) ⊕ Ñil∗−1(R) involving the same Ñilgroups. I Motivation from
Universal deformation rings for dihedral 2groups
 J. London Math Soc
"... Abstract. Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose D is a dihedral 2group. We prove that the universal deformation ring R(D, V) of an endotrivial kDmodule V is always isomorphic to W[Z/2 × Z/2]. As a consequence we ..."
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Cited by 5 (5 self)
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Abstract. Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose D is a dihedral 2group. We prove that the universal deformation ring R(D, V) of an endotrivial kDmodule V is always isomorphic to W[Z/2 × Z/2]. As a consequence we
DIHEDRAL COVERINGS OF TRIGONAL CURVES
"... Abstract. We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curveD with a singular point of multiplicity (degD−3). 1. ..."
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Cited by 2 (2 self)
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Abstract. We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curveD with a singular point of multiplicity (degD−3). 1.
Results 1  10
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737,278