arXiv research

Researchers solved the multiple fibration problem for Seifert 3-orbifolds.

Let $M$ be a closed 4-manifold with $π_2(M)\cong{Z}$. Then $M$ is homotopy equivalent to either $CP^2$, or the total space of an orbifold bundle with general fibre $S^2$ over a 2-orbifold $B$, or the total space of an $RP^2$-bundle over an aspherical surface. If $π=π_1(M)\not=1$ there are at most two such bundle spaces…

A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirr…

This paper determines the flexible exponent for non-geometric 3-manifolds.

We prove that there exists a positive, explicit function $F(k, E)$ such that, for any group $G$ admitting a $k$-acylindrical splitting and any generating set $S$ of $G$ with $\mathrm{Ent}(G,S)<E$, we have $|S| \leq F(k, E)$. We deduce corresponding finiteness results for classes of groups possessing acylindrical splitt…

We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of 3--manifold groups in all but a few exceptional cases.

We study a particular class of supersymmetric M-theory eight-dimensional non-geometric compactification backgrounds to three-dimensional Minkowski space-time, proving that the global space of the non-geometric compactification is still a differentiable manifold, although with very different geometric and topological pr…

Unfolding paths in Outer space accumulate on a simplex, not converge.

We study Riemannian metrics on compact, torsionless, non-geometric $3$-manifolds, i.e. whose interior does not support any of the eight model geometries. We prove a lower bound "à la Margulis" for the systole and a volume estimate for these manifolds, only in terms of an upper bound of entropy and diameter. We then ded…

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

In this technical note, we adapt an idea of Gabai to construct non-uniquely ergodic, non-geometric, arational trees.

Novel approach to financial derivatives pricing using rough path theory.

We study ten-dimensional supersymmetric vacua with NSNS non-geometric fluxes, in the framework of $β$-supergravity. We first provide expressions for the fermionic supersymmetry variations. Specifying a compactification ansatz to four dimensions, we deduce internal Killing spinor equations. These supersymmetry condition…

Recently, Ian Agol introduced a class of "veering" ideal triangulations for mapping tori of pseudo-Anosov homeomorphisms of surfaces punctured along the singular points. These triangulations have very special combinatorial properties, and Agol asked if these are "geometric", i.e. realised in the complete hyperbolic met…

We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with respect to the two natural torsionful connections $\nabla^{(\pm)}$ that arise in the …

We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.

We give a systematic derivation of the local expressions of the NS H-flux, geometric F- as well as non-geometric Q- and R-fluxes in terms of bivector beta- and two-form B-potentials including vielbeins. They are obtained using a supergeometric method on QP-manifolds by twist of the standard Courant algebroid on the gen…

New framework robustly handles outliers in Wasserstein DRO for better decision-making.

We present a ten-dimensional theory, named β-supergravity, that contains non-geometric fluxes and could uplift some four-dimensional gauged supergravities. Building on earlier work, we study here its NSNS sector, where Q- and R-fluxes are precisely identified. Interestingly, the Q-flux is captured in an analogue of the…

We review a systematic construction of the 2-stack of bundle gerbes via descent, and extend it to non-abelian gerbes. We review the role of non-abelian gerbes in orientifold sigma models, for the anomaly cancellation in supersymmetric sigma models, and in a geometric description of so-called non-geometric T-duals.

Let $g \colon S \looparrowright N$ be a properly immersed $π_1$--injective surface in a non-geometric $3$--manifold $N$. We compute the distortion of $π_1(S)$ in $π_1(N)$ and show that how it is related to separability of $π_1(S)$ in $π_1(N)$. The only possibility of the distortion is linear, quadratic, exponential, an…

In this paper, it is shown that every orientable closed 3-manifold maps with nonzero degree onto at most finitely many homeomorphically distinct irreducible non-geometric orientable closed 3-manifolds. Moreover, given any nonzero integer, as a mapping degree up to sign, every orientable closed 3-manifold maps with that…

Motivated by the quest to understand the analog of non-geometric flux compactification in the context of M-theory, we study higher dimensional analogs of generalized Poisson sigma models and corresponding dual string and p-brane models. We find that higher generalizations of the algebraic structures due to Dorfman, Roy…

The paper studies orbifold braid groups and their properties.

Study shortest non-simple geodesics on 2-orbifolds, finding unique shortest curve.

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality and has a natural ring structure. Some examples of orbifold cohomology ring are c…

We give hodge structures on quasitoric orbifolds. We define orbifold hodge numbers and show a correspondence of orbifold hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend hodge structures to a non complex setting .

The abstract constructs a set of bad 3-orbifolds and shows how any bad 3-orbifold can be transformed into a good one.

We construct several families of embeddings of braid groups into mapping class groups of orientable and non-orientable surfaces and prove that they induce the trivial map in stable homology in the orientable case, but not so in the non-orientable case. We show that these embeddings are non-geometric in the sense that t…

The paper classifies fibrations of 3-dimensional flat orbifolds.

Study on embedding hyperbolic 2-orbifolds in Bianchi orbifolds.

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold homeomorphism types. This is a generalization to the orbifold category of a similar result …

Study of orbifold Chern character using superconnections.

Study topological quantum mechanics on orbifolds with geometric interpretation.

We investigate geometric aspects of double field theory (DFT) and its formulation as a doubled membrane sigma-model. Starting from the standard Courant algebroid over the phase space of an open membrane, we determine a splitting and a projection to a subbundle that sends the Courant algebroid operations to the correspo…

We prove that a connected 2-dimensional orbifold with finitely generated and infinite orbifold fundamental group is good. We also describe all the good 2-dimensional orbifolds with finite orbifold fundamental groups

The study examines Eschenburg orbifolds with positive sectional curvature and their geometric/topological properties.

We introduce the $Γ$-Euler-Satake characteristics of a general orbifold $Q$ presented by an orbifold groupoid $\mathcal{G}$, generalizing to orbifolds that are not necessarily global quotients the generalized orbifold Euler characteristics of Bryan-Fulman and Tamanoi. Each of these Euler characteristics is defined as t…

Highly connected orbifolds are rare but exist.

We proved the convergence of a sequence of 2 dimensional comapct Kahler-Einstein orbifolds with rational quotient singularities and with some uniform bounds on the volumes and on the Euler characteristics of our orbifods to a Kahler-Einstein 2-dimensional orbifold. Our limit orbifold can have worse singularities than t…

The paper studies orbifold splice quotients and log covers of surface pairs.

This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne orbifold cohomology, Cheeger-Simons orbifold cohomology and string connections.

Unified theory of orbifolds and cohomology.

We characterize Riemannian orbifolds and their coverings in terms of metric geometry. In particular, we show that the metric double of a Riemannian orbifold along the closure of its codimension one stratum is a Riemannian orbifold and that the natural projection is an orbifold covering.

For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is equivalent to a strong equivariant immersion.

We prove that Demailly's holomorphic Morse inequalities hold true for complex orbifolds by using a heat kernel method. Then we introduce the class of Moishezon orbifolds and as an application of our inequalties, we give a geometric criterion for a compact connected orbifold to be a Moishezon orbifolds, thus generalizin…

This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability class contains a unique minimal element, whereas the class of Seifert manifolds …

We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that orbifolds of only finitely many orbifold diffeomorphism types may arise in any collecti…