Related papers: Power operations in orbifold Tate K-theory

We study the operational bivariant theory associated to the covariant theory of Grothendieck groups of coherent sheaves, and prove that it has many geometric properties analogous to those of operational Chow theory. This operational…

The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations,…

We analyze the structure of the virtual (orbifold) K-theory ring of the complex orbifold P(1,n) and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin-Graham. In particular, we identify the…

We calculate the $K(n-1)$-localized $E_n$ theory for symmetric groups, and deduce a modular interpretation of the total power operation $\psi^p_F$ on $F=L_{K(n-1)}E_n$ in terms of augmented deformations of formal groups and their subgroups.…

The operad of moulds is realized in terms of an operational calculus of formal integrals (continuous formal power series). This leads to many simplifications and to the discovery of various suboperads. In particular, we prove a conjecture…

This paper introduces and investigates the class of \textit{$k$-quasi $n$-power posinormal operators} in Hilbert spaces, generalizing both posinormal and $n$-power posinormal operators. We establish fundamental properties including matrix…

We compute $K$-theory invariants of algebras of pseudodifferential operators on manifolds with corners and prove an equivariant index theorem for operators invariant with respect to an action of $\R^k.$ We discuss the relation between our…

We consider categories of equivariant mixed Tate motives, where equivariant is understood in the sense of Borel. We give the two usual definitions of equivariant motives, via the simplicial Borel construction and via algebraic…

We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to…

We present the theory of pseudodifferential operators acting on a vector orbibundle over an orbifold, construct the zeta function of an elliptic pseudodifferential operator and show the existence of a meromorphic extension to the complex…

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.

For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and…

Power operations in the homology of infinite loop spaces, and $H_\infty$ or $E_\infty$ ring spectra have a long history in Algebraic Topology. In the case of ordinary mod p homology for a prime p, the power operations of Kudo, Araki, Dyer…

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…

We construct and study an algebraic theory which closely approximates the theory of power operations for Morava E-theory, extending previous work of Charles Rezk in a way that takes completions into account. These algebraic structures are…

We show that the Adams operations in complex K-theory lift to operations in smooth K-theory. The main result is a Riemann-Roch type theorem about the compatibility of the Adams operations and the integration in smooth K-theory.

We construct a family of additive endomorphisms $\Psi_k, k=1, 2...$ of the Grothendieck ring of quasiprojective varieties and the Grothendieck ring of Chow motives similar to the Adams operations in the K-theory. The speciality of the…

In this paper we compute the total power operation for the Morava $E$-theory of any finite group up to torsion. Our formula is stated in terms of the $GL_n(Q_p)$-action on the Drinfeld ring of full level structures on the formal group…

We provide a general framework for wall-crossing of equivariant K-theoretic enumerative invariants of appropriate moduli stacks $\mathfrak{M}$, by lifting Joyce's homological universal wall-crossing arXiv:2111.04694 to K-theory and to…

Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.