Related papers: A note on invariant description of $SU(2)$-structu…
We extend Turaev's definition of torsion invariants of 3-dimensional manifolds equipped with non-singular vector fields, by allowing (suitable) tangency circles to the boundary, and manifolds with non-zero Euler characteristic. We show that…
Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…
Consider a Riemannian spin manifold $(M^{n}, g)$ $(n\geq 3)$ endowed with a non-trivial 3-form $T\in\Lambda^{3}T^{*}M$, such that $\nabla^{c}T=0$, where $\nabla^{c}:=\nabla^{g}+\frac{1}{2}T$ is the metric connection with skew-torsion $T$.…
A constructive approach to differential calculus on quantum principal bundles is presented. The calculus on the bundle is built in an intrinsic manner, starting from given graded (differential) *-algebras representing horizontal forms on…
We provide a unified description of the three covariant superspace approaches to ${\cal N}=2$ conformal supergravity in four dimensions: (i) conformal superspace; (ii) $\mathsf{U}(2)$ superspace; and (iii) $\mathsf{SU}(2)$ superspace. Each…
We use the $\eta$ invariants of spin$^c$ Dirac operators to distinguish connected components of moduli spaces of Riemannian metrics with positive Ricci curvature. We then find infinitely many non-diffeomorphic five dimensional manifolds for…
All supersymmetric gauge theories based on simple groups which have an affine quantum moduli space, i.e. one generated by gauge invariants with no relations, W=0, and anomaly matching at the origin, are classified. It is shown that the only…
We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian…
Possible quantum mechanical corollaries of changing the vectorial geometrical model of the physical space, extending it twice, in order to describe its spinor structure (in other terminology and emphasis it is known as the Hopf's bundle)…
We study the geometry of type II supergravity compactifications in terms of an oriented vector bundle $E$, endowed with a bundle metric of split signature and further datum. The geometric structure is associated with a so-called generalised…
We study the ring of invariant functions over the $N$-fold Cartesian product of copies of the compact Lie group $G=SU(2)$, modulo the action of conjugation by the diagonal subgroup, generalizing the group character ring. For $N=1$, an…
The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual…
We perform a systematic exact algebraic search for integrable spin-S chains which are isotropic in spin space, i.e. are su(2)-invariant. The families of spin chains found for S < 14 support recent arguments in favour of the complete…
A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…
Killing spinor identities relate components of equations of motion to each other for supersymmetric backgrounds. The only input required is the field content and the supersymmetry transformations of the fields, as long as an on-shell…
We consider 5d $\mathcal{N}=1$ SU(2) super Yang-Mills theory on $X\times S^1$, with $X$ a closed smooth four-manifold. A partial topological twisting along $X$ renders the theory formally independent of the metric on $X$. The theory depends…
We study compactifications of type IIA supergravity on six-dimensional manifolds with SU(2) structure and compute the low-energy effective action in terms of the non-trivial intrinsic torsion. The consistency with gauged N=4 supergravity is…
This is the second of a series of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks. Using the notion of obstruction…
Motivated by the Turaev-Viro invariant of 3-manifolds, we construct a formal topological invariant of closed, oriented 3-manifolds involving spherical tetrahedra as an application of the asymptotic formula of 6j symbols for the Quantum…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…