Related papers: Gysin exact sequences for quantum weighted lens sp…
By a diagonal embedding of $U(1)$ in $SU_q(m)$, we prolongate the diagonal circle action on the Vaksman-Soibelman quantum sphere $S^{2n+1}_q$ to the $SU_q(m)$-action on the prolongated bundle. Then we prove that the noncommutative vector…
The full asymptotic expansion of the equivariant complex Ray-Singer torsion for high powers of line bundles on symmetric spaces is given in an explicit form. In the case of isolated fixed points this expansion is given for general complex…
In the high-energy quantum-physics literature one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as…
Let $G_{n,k}$ denote the real Grassmann manifold of $k$-dimensional vector subspaces of $\mathbb R^n$. Using the Hodgkin spectral sequence, we compute the complex $K$-ring of $G_{n,k}$, up to a small indeterminacy, for all values of $n,k$…
A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). For a representable ring cohomology theory A(-) with a special linear orientation and…
The phase space of the Wess-Zumino-Witten model on a circle with target space a compact, connected, semisimple Lie group $G$ is defined and the corresponding symplectic form is given. We present a careful derivation of the Poisson brackets…
We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
The truncation in the number of single-trace chiral primary operators of $\N=4$ SYM and its conjectured connection with gravity on quantum spacetimes are elaborated. The model of quantum spacetime we use is $AdS^5_q \times S^5_q$ for $q$ a…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…
We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of…
The structure of quantum principal bundles is studied, from the viewpoint of Tannaka-Krein duality theory. It is shown that if the structure quantum group is compact, principal G-bundles over a quantum space M are in a natural…
We give a construction of the moduli space of stable maps to the classifying stack B\mu_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed formula for the total Chern class of \mu_r-eigenspaces of…
We interpret certain equivariant Kasparov groups as equivariant representable K-theory groups. We compute these groups via a classifying space and as K-theory groups of suitable sigma-C*-algebras. We also relate equivariant vector bundles…
We use our recently developed algebraic methods for the calculation of the heat kernel on homogeneous bundles over symmetric spaces to evaluate the non-perturbative low-energy effective action in quantum general relativity and Yang-Mills…
The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the…