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Hermitian Ktheory of the integers
 Amer. J. Math
"... Abstract. Rognes and Weibel used Voevodsky’s work on the Milnor conjecture to deduce the strong DwyerFriedlander form of the LichtenbaumQuillen conjecture at the prime 2. In consequence (the 2completion of) the classifying space for algebraic Ktheory of the integers Z[1/2] can be expressed as a ..."
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Abstract. Rognes and Weibel used Voevodsky’s work on the Milnor conjecture to deduce the strong DwyerFriedlander form of the LichtenbaumQuillen conjecture at the prime 2. In consequence (the 2completion of) the classifying space for algebraic Ktheory of the integers Z[1/2] can be expressed as a fiber product of wellunderstood spaces BO and BGL(F3) + over BU. Similar results are now obtained for Hermitian Ktheory and the classifying spaces of the integral symplectic and orthogonal groups. For the integers Z[1/2], this leads to computations of the 2primary Hermitian Kgroups and affirmation of the LichtenbaumQuillen conjecture in the framework of Hermitian Ktheory.
RAMONDRAMOND FIELDS, FRACTIONAL BRANES AND ORBIFOLD DIFFERENTIAL KTHEORY
, 2007
"... We study Dbranes and RamondRamond fields on global orbifolds of Type II string theory with vanishing Hflux using methods of equivariant Ktheory and Khomology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct co ..."
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We study Dbranes and RamondRamond fields on global orbifolds of Type II string theory with vanishing Hflux using methods of equivariant Ktheory and Khomology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the lowenergy effective field theory, and which provides new consistency conditions for fractional Dbranes and RamondRamond fields on orbifolds. We use an equivariant Chern character from equivariant Ktheory to Bredon cohomology to define new RamondRamond couplings of Dbranes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant Ktheory. We derive a Dirac quantization rule for RamondRamond fluxes, and study flat RamondRamond potentials on orbifolds.
EQUIVARIANT KTHEORY OF FINITE DIMENSIONAL REAL VECTOR SPACES
, 903
"... Abstract. We give a general formula for the equivariant complex Ktheory K ∗ G (V) of a finite dimensional real linear space V equipped with a linear action of a compact group G in terms of the representation theory of a certain double cover of G. Using this general formula, we give explicit computa ..."
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Abstract. We give a general formula for the equivariant complex Ktheory K ∗ G (V) of a finite dimensional real linear space V equipped with a linear action of a compact group G in terms of the representation theory of a certain double cover of G. Using this general formula, we give explicit computations in various interesting special cases. In particular, as an application we obtain explicit formulas for the Ktheory of C ∗ r (GL(n, R)), the reduced group C*algebra of GL(n, R). Let G be a compact group acting linearly on the real vector space V. In this paper we want to give explicit formulas for the complex equivarant Ktheory K ∗ G (V) depending on the action of the given group G on V. By use of the positive solution of the ConnesKasparov conjecture in [5], this will also provide explicit formulas