Related papers: Non-split superstrings of dimension $(1|2)$
Motivated by a valuation theorem, recently obtained by Rangachev, we study the \'etale extensions $A\subset B$ of polynomial rings over an algebraically closed field of characteristic zero, such that the integral closure $\overline{A}$ is a…
In this paper we introduce a superclass of split digraphs, which we call spine digraphs. Those are the digraphs D whose vertex set can be partitioned into two sets X and Y such that the subdigraph induced by X is traceable and Y is a stable…
In Physics and in Mathematics $\mathbb{Z}_2^n$-gradings, $n>1$, appear in various fields. The corresponding sign rule is determined by the `scalar product' of the involved $\mathbb{Z}_2^n$-degrees. The $\mathbb{Z}_2^n$-Supergeometry…
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as…
One of the subtleties that has made superstring perturbation theory intricate at high string loop order is the fact that as shown by Donagi and Witten, supermoduli space is not holomorphically projected, nor is it holomorphically split. In…
We consider partial supersymmetry breaking in ${\cal N}=2$ supergravity coupled to a single vector and a single hypermultiplet. This breaking pattern is in principle possible if the quaternion-K\"ahler space of the hypermultiplet admits (at…
Let $X$ be a proper CAT($0$) space and $G$ a cocompact group of isometries of $X$ without fixed point at infinity. We prove that if $\partial X$ contains an invariant subset of circumradius $\pi/2$, then $X$ contains a quasi-dense, closed…
We chart the classical moduli space of heterotic strings with broken supersymmetry a la Scherk-Schwarz and gauge group rank reduced by 8 in eight dimensions. This space consists of four connected components, each with its own characteristic…
We show the existence of a supersymmetry breaking mechanism in string theory, where N=4 supersymmetry is broken spontaneously to N=2 and N=1 with moduli dependent gravitino masses. The spectrum of the spontaneously broken theory with lower…
We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of…
We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays…
The condition of having an $N=1$ spacetime supersymmetry for heterotic string leads to 4 distinct possibilities for compactifications namely compactifications down to 6,4,3 and 2 dimensions. Compactifications to 6 and 4 dimensions have been…
The paper provides computations of the first non-vanishing $\mathbb{A}^1$-homotopy sheaves of the orthogonal Stiefel varieties which are relevant for the unstable isometry classification of quadratic forms over smooth affine schemes over…
The Steenrod problem for closed orientable manifolds was solved completely by Thom. Following this approach, we solve the Steenrod problem for closed orientable orbifolds, proving that the rational homology groups of a closed orientable…
Generalizing Heegaard splittings of 3-manifolds and trisections of 4-manifolds, we consider multisections of higher-dimensional smooth (or PL) closed orientable manifolds, namely decompositions into 1-handlebodies whose subcollections…
The geometric features and toric descriptions of two different 8-dimensional $Spin(7)$ manifolds constructed via distinct resolutions of the cone over an $SU(3)/U(1)$ base, reveals that the geometry of the $Spin(7)$ conifold transition…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…
This is the beginning of an obstruction theory for deciding whether a map f:S^2 --> X^4 is homotopic to a topologically flat embedding, in the presence of fundamental group and in the absence of dual spheres. The first obstruction is Wall's…
We show that the moduli space of nonnegatively curved metrics on each member of a large class of 2-connected 7-manifolds, including each smooth manifold homeomorphic to $S^7$, has infinitely many connected components. The components are…
We construct germs of complex manifolds of dimension $m$ along projective submanifolds of dimension $n$ with ample normal bundle and without non-constant meromorphic functions whenever $m \geq 2n$. We also show that our methods do not allow…