A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Constructs modular forms and proves divisibility results for odd-dimensional manifolds.
For odd-dimensional spheres, there's always a second short geodesic.
Study proves higher-order conformal forms don't exist in odd dimensions.
We define and discuss an extension of the SpinC quantization concept to odd-dimensional manifolds. After that we describe its relation to (the usual) even-dimensional SpinC quantization and how its famous properties like "Quantization commutes with reduction" can be regained in odd dimensions. At the end, we analyze th…
New proof of Llarull's rigidity theorem in odd dimensions via spectral flow.
We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd Chern classes for cocycles in odd -theory. Moreover we discover that in odd dimen…
Rigidity theorem for scalar curvature on odd-dimensional singular manifolds.
Proves two theorems on odd-dimensional manifolds with boundary.
Odd-dimensional manifolds have contact maps of non-zero degree.
New contact manifolds with many fillings found.
We determine the minimal volume of arithmetic hyperbolic orientable n-dimensional orbifolds (compact and non-compact) for every odd dimension n>3. Combined with the previously known results it solves the minimal volume problem for arithmetic hyperbolic n-orbifolds in all dimensions.
New formulas derived for anomaly cancellation using modular forms and E8 bundles.
Magnitude of Euclidean domains predicts Willmore energy in odd dimensions.
New Sasaki structures identified by Hodge numbers in odd dimensions.
New nonacyclic Reidemeister torsions defined for odd-dimensional manifolds.
A recent anomaly computation of Horava and Witten is proved and generalized in the form of two index theorems in odd dimensions. Theorem A is a fixed point formula for orientation-reversing involutions. Theorem B is an index theorem for manifolds with boundary using local boundary conditions. Both hold for families of …
It is well-known that odd-dimensional manifolds have Euler characteristic zero. Furthemore orientable manifolds have an even Euler characteristic unless the dimension is a multiple of . We prove here a generalisation of these statements: a -orientable manifold (or more generally Poincaré complex) has even Euler c…
Smooth SE structures on Sasaki-joins and Bott orbifolds constructed.
The study finds infinitely many different geometries for odd-dimensional manifolds with positive Ricci curvature.
Two-root Riemannian manifolds have no odd-dimensional examples.
Study spectral flow for Callias operators to prove obstructions to positive scalar curvature.
Odd connections on supermanifolds are defined and their properties studied.
Functional determinant for mixed signature sphere products depends on sphere dimensions and parity.
Let M be a closed compact n-dimensional manifold with n odd. We calculate the first and second variations of the zeta-regularized determinants det^\primeΛand det L as the metric on M varies, where Δdenotes the Laplacian on functions and L denotes the conformal Laplacian. We see that the behavior of these functionals de…
The L^2-torsion is an invariant defined for compact L^2-acyclic manifolds of determinant class, for example odd dimensional hyperbolic manifolds. It was introduced by John Lott and Varghese Mathai and computed for hyperbolic manifolds in low dimensions. In this paper we show that the L^2-torsion of hyperbolic manifolds…
Develops a method to construct entire minimal graphs of odd dimensions.
It is well known that the Euler characteristic of an odd dimensional compact manifold is zero. An Euler complex is a combinatorial analogue of a compact manifold. We present here an elementary proof of the corresponding result for Euler complexes.
We construct examples in any odd dimension of contact manifolds with finite and non-zero algebraic torsion (in the sense of Latschev-Wendl), which are therefore tight and do not admit strong symplectic fillings. We prove that Giroux torsion implies algebraic -torsion in any odd dimension, which proves a conjecture b…
Non-vanishing steady Euler flows and Beltrami fields found in high dimensions.
We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that …
Study odd generalized Einstein metrics on 3D Lie groups.
We show that C^2 conformally compact Riemannian Einstein metrics have conformal compactifications that are smooth up to the boundary in dimension 3 and all even dimensions, and polyhomogeneous in odd dimensions greater than 3.
In this paper, we use Chas-Sullivan theory on loop homology and Leray-Serre spectral sequence to investigate the topological structure of the non-contractible component of the free loop space on the real projective spaces with odd dimensions. Then we apply the result to get the resonance identity of non-contractible ho…
Formulas for spectra of higher spin operators on sphere subbundles.
In this paper we give a proof of the Lefschetz fixed point formula of Freed for an orientation-reversing involution on an odd dimensional spin manifold by using the direct geometric method introduced in [2] and then we generalize this formula under the noncommutative geometry framework.
We impose constraints on the odd coordinates of super Teichmüller space in the uniformization picture for the monodromies around Ramond punctures, thus reducing the overall odd dimension to be compatible with that of the moduli spaces of super Riemann surfaces. Namely, the monodromy of a puncture must be a true parabol…
The aim of this paper is to formulate a local systolic inequality for odd-symplectic forms (also known as Hamiltonian structures) and to establish it in some basic cases. Let be an odd-symplectic form on an oriented closed manifold of odd dimension. We say that is Zoll if the trajectories of the flow given …
We prove the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres in all odd dimensions greater than 3. In dimension 5 we obain somewhat sharper results. There are examples where the number of effective parameters in the Einstein metric grows exponentially with dimension.
We prove that, under reasonable conditions, odd co-dimension Riemannian foliations cannot occur in positively curved manifolds.
As was recently observed by M. Xu and J. Wolf, there is a gap in Berard Bergery's classification of odd dimensional positively curved homogeneous spaces. Since this classification has been used in other papers as well, we give a modern, complete and self contained proof (in odd as well as even dimensions), confirming t…
Study finds infinite families of Sasaki-Einstein metrics on spheres.
An example of a three dimensional flat paracontact metric manifold with respect to Levi-Civita connection is constructed. It is shown that no such manifold exists for odd dimensions greater than or equal to five.
We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following two conditions: the pencil of 2-forms associated with the corresponding Pfaffian …
We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the structure.
We prove the existence of exotic but homotopically trivial contact structures on spheres of dimension 8k-1. Together with previous results of Eliashberg and the second author this establishes the existence of such structures on all odd-dimensional spheres (of dimension at least 3).
We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas-Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products. Using this theory we construct positive scalar curvature metrics on closed smooth manifolds of dimension at least five which ha…
The functional determinants of the GJMS scalar operators, P_{2k}, on even-dimensional spheres are computed via Barnes multiple gamma functions relying on the numerical availability of the digamma function. For the critical k=d/2 case, it is necessary to calculate the Stirling moduli. The multiplicative anomalies are gi…
The Yamabe invariant is an invariant of a closed smooth manifold defined using conformal geometry and the scalar curvature. Recently, Petean showed that the Yamabe invariant is non-negative for all closed simply connected manifolds of dimension . We extend this to show that Yamabe invariant is non-negative for a…