Related papers: An Operator model for connective K-theory with rea…
We define and study the quantum equivariant $K$-theory of cotangent bundles over Grassmannians. For every tautological bundle in the $K$-theory we define its one-parametric deformation, referred to as quantum tautological bundle. We prove…
For a cyclic group $C_n$, we identify Greenlees' equivariant connective K theory spectrum $kU_{C_n}$ as an $RO(C_n)$-graded localization of the actual connective cover of $KU_{C_n}$.
A K-theoretic counterpart of quantum cohomology theory is discussed.
We construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion and define the associated push-forward which satisfies functoriality, compatibility with…
In this paper, we describe necessary and sufficient conditions for a binormal or complex symmetric operator to have the other property. Along the way, we find connections to the Duggal and Aluthge transforms, and give further properties of…
The aim of this paper is to describe the torus equivariant $K$-ring of even-dimensional complex quadrics by studying the graph equivariant $K$-theory of their corresponding GKM graphs. This involves providing a presentation for its graph…
We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting…
Algebraic K-theory is the stable homotopy theory of homotopy theories, and it interacts with algebraic structures accordingly. In particular, we prove the Deligne Conjecture for algebraic K-theory.
We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb like potentials) on pseudosphere and compare their spectra and the sets of…
We consider the class of bounded symmetric anti-linear operators $B$ with a cyclic vector. We associate with $B$ the spectral data consisting of a probability measure and a function. In terms of the spectral data of $B$, we introduce a…
We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have \textit{even-form} and \textit{odd-form} symmetries determined by $K_N(\partial X)$, the twisted K-theory as D-brane charges on the…
We prove that any spectrum is equivalent to the nonconnective K-theory of a stable $\infty$-category. We use these results to construct a stable $\infty$-category $\mathcal{C}$ with a bounded t-structure such that…
In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D)…
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a…
We introduce a theory of syntomic cohomology for ring spectra with involution, which we call Real syntomic cohomology. We show that our construction extends the theory of syntomic cohomology for rings with involution due to Park. Our…
We prove that united K-theory is a surjective functor from the category of real simple purely infinite C*-algebras to the cateogry of countable acyclic CRT-modules.
We prove a perturbative inversion theorem for the map between the interacting and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and short-range interactions between the fermions.…
In this note we obtain commutativity criteria for normal compact operators using the projective spectrum. We thus improve a corresponding result obtained by Chagouel, Stessin and Zhu[Trans AMS,2016].
We generalize Blumberg-Mandell's K-theoretic Poitou-Tate duality to arithmetic schemes of arbitrary dimension, smooth and proper over S-integers. As in our earlier papers on the subject, we discuss how to model the compactly supported side…
This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in the relative situation over a noncentral, noncommutative, nonsemisimple base ring, as announced in Section 0.4 of arXiv:0708.3398. We prove the…