1,316 research outputs found
Equivariant Cohomological Chern Characters
We construct for an equivariant cohomology theory for proper equivariant
CW-complexes an equivariant Chern character, provided that certain conditions
about the coefficients are satisfied. These conditions are fulfilled if the
coefficients of the equivariant cohomology theory possess a Mackey structure.
Such a structure is present in many interesting examples.Comment: 30 page
Index of transversally elliptic operators
In 1996, Berline and Vergne gave a cohomological formula for the index of a
transversally elliptic operator. In this paper we propose a new point of view
where the cohomological formulae make use of equivariant Chern characters with
generalized coefficients and with compact suppport. This kind of Chern
characters was studied by the authors in a previous paper (see
arXiv:0801.2822).Comment: 41 page
Orbifold index and equivariant K-homology
We consider a invariant Dirac operator D on a manifold with a proper and
cocompact action of a discrete group G. It gives rise to an equivariant
K-homology class [D]. We show how the index of the induced orbifold Dirac
operator can be calculated from [D] via the assembly map. We further derive a
formula for this index in terms of the contributions of finite cyclic subgroups
of G. According to results of W. Lueck, the equivariant K-homology can
rationally be decomposed as a direct sum of contributions of finite cyclic
subgroups of G. Our index formula thus leads to an explicit decomposition of
the class [D].Comment: minor correction in Sec.3.
The cohomological Hall algebra of a preprojective algebra
We introduce for each quiver and each algebraic oriented cohomology
theory , the cohomological Hall algebra (CoHA) of , as the -homology
of the moduli of representations of the preprojective algebra of . This
generalizes the -theoretic Hall algebra of commuting varieties defined by
Schiffmann-Vasserot. When is the Morava -theory, we show evidence that
this algebra is a candidate for Lusztig's reformulated conjecture on modular
representations of algebraic groups.
We construct an action of the preprojective CoHA on the -homology of
Nakajima quiver varieties. We compare this with the action of the Borel
subalgebra of Yangian when is the intersection theory. We also give a
shuffle algebra description of this CoHA in terms of the underlying formal
group law of . As applications, we obtain a shuffle description of the
Yangian.Comment: V6: 44 pages; section 6 added; errors in section 8 corrected; minor
revisions throughout; final versio
Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory
We study D-branes and Ramond-Ramond fields on global orbifolds of Type II
string theory with vanishing H-flux using methods of equivariant K-theory and
K-homology. 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 low-energy effective field theory,
and which provides new consistency conditions for fractional D-branes and
Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from
equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings
of D-branes which generalize previous examples. We propose a definition for
groups of differential characters associated to equivariant K-theory. We derive
a Dirac quantization rule for Ramond-Ramond fluxes, and study flat
Ramond-Ramond potentials on orbifolds.Comment: 46 pages; v2: typos correcte
Leading terms of Artin L-series at negative integers and annihilation of higher K-groups
Let L/K be a finite Galois extension of number fields with Galois group G. We use leading terms of Artin L-series at strictly negative integers to construct elements which
we conjecture to lie in the annihilator ideal associated to the Galois action on the higher dimensional algebraic K-groups of the ring of integers in L. For abelian G our conjecture coincides with a conjecture of Snaith and thus generalizes also the well known Coates-Sinnott conjecture. We show that our conjecture is implied by the appropriate special case of the equivariant Tamagawa number conjecture (ETNC) provided that the Quillen-Lichtenbaum conjecture holds. Moreover, we prove induction results for the ETNC in the case of Tate motives h0(Spec(L))(r), where r is a strictly negative integer. In particular, this implies the ETNC for the pair (h0(Spec(L))(r),M), where L is totally real, r < 0 is odd and M is a maximal order containing Z[ 1/2 ]G, and will also provide some evidence for our conjecture
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