arXiv research

Study maximal antipodal sets in exceptional symmetric spaces.

New method bounds graph curvature with exceptions.

The study examines exceptional sets for radial limits of superharmonic functions on curved manifolds.

The paper strengthens a theorem on crossings under linear perturbations with Hausdorff measure estimates.

Concerning the set of exceptional surgery slopes for a hyperbolic knot, Lackenby and Meyerhoff proved that the maximal cardinality is 10 and the maximal diameter is 8. Their proof is computer-aided in part, and both bounds are achieved simultaneously. In this note, it is observed that the diameter bound 8 implies the m…

It has been observed that most manifolds in the Callahan-Hildebrand-Weeks census of cusped hyperbolic $3$-manifolds are obtained by surgery on the minimally twisted 5-chain link. A full classification of the exceptional surgeries on the 5-chain link has recently been completed. In this article, we provide a complete cl…

Unified solution to M-theory problems using super-exceptional geometry.

Study on regularity of exceptional actions and moduli of continuity for circle diffeomorphisms.

Study geodesic trees and exceptional directions in FPP on hyperbolic groups.

The paper optimizes exceptions in a statistical production system using machine learning.

Study shows area-minimizing submanifolds are mostly smooth except for specific types.

Study shows area-minimizing submanifolds are mostly smooth except for geodesics, minimal surfaces, and hypersurfaces.

This paper is based on a previous publication [29]. Our work extends exception mining and outlier detection to the case of object-relational data. Object-relational data represent a complex heterogeneous network [12], which comprises objects of different types, links among these objects, also of different types, and at…

A new quantum relation connects exceptional Lie algebras and knots.

Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constraints can be realized by some branched cover. We connect recent development in spherical conic metrics to this old problem, and give a new m…

We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL(2;C)-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We al…

Classifies exceptional Legendrian realizations of Hopf link connected sums.

New robust algorithms improve learning with feature feedback.

We give an explicit classification of maximal antipodal sets in any irreducible compact symmetric space except for spin groups and half spin groups, and some quotient symmetric spaces associated to them.

Complete exceptional surgeries identified for two-bridge links.

We study a class of exceptional minimal surfaces in spheres for which all Hopf differentials are holomorphic. Extending results of Eschenburg and Tribuzy \cite{ET0}, we obtain a description of exceptional surfaces in terms of a set of absolute value type functions, the $a$-invariants, that determine the geometry of the…

A closed hyperbolic 3-manifold is exceptional if its shortest geodesic does not have an embedded tube of radius $\ln(3)/2$. D. Gabai, R. Meyerhoff and N. Thurston identified seven families of exceptional manifolds in their proof of the homotopy rigidity theorem. They identified the hyperbolic manifold known as Vol3 in …

Proves a theorem for Assouad dimension with applications to distance sets and radial projections.

Combining M-algebra and hyperbolic involutory algebra extends exceptional tangent spaces to 11 dimensions.

We consider in this paper the minimally twisted chain link with 5 components in the 3-sphere, and we analyze the Dehn surgeries on it, namely the Dehn fillings on its exterior M5. The 3-manifold M5 is a nicely symmetric hyperbolic one, filling which one gets a wealth of hyperbolic 3-manifolds having 4 or fewer (includi…

The paper constructs gravitational instantons with unique collapse patterns.

Study shows instability of certain MOTSs with continuous symmetry.

We give a complete classification of exceptional surgeries on hyperbolic alternating knots in the 3-sphere. As an appendix, we also show that the Montesinos knots M (-1/2, 2/5, 1/(2q + 1)) with q at least 5 have no non-trivial exceptional surgeries. This gives the final step in a complete classification of exceptional …

Study braid group actions on exceptional sequences using branched coverings.

The study bounds exceptional surgeries for hyperbolic knots.

Study of exceptional algebroids in relation to type IIB superstrings.

We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $α$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.

The paper refines a conjecture about Fano varieties' quantum cohomology and exceptional collections.

This paper concerns the truly or purely cosmetic surgery conjecture. We give a survey on exceptional surgeries and cosmetic surgeries. We prove that the slope of an exceptional truly cosmetic surgery on a hyperbolic knot in $S^3$ must be $\pm 1$ and the surgery must be toroidal but not Seifert fibred. As consequence we…

We determine the Thurston's geometry possesed by any Seifert fibered conemanifold structure in a Seifert manifold with orbit space $S^2$ and no more than three exceptional fibres, whose singular set, composed by fibres, has at most 3 components which can include exceptional or general fibres (the total number of except…

No exceptional orbits found in Hilbert spaces actions.

The study lists all exceptional Dehn fillings on specific 3-manifolds.

Study classifies exceptional surgeries on specific links.

Survey article on recent Kähler geometry and exceptional holonomy.

A Dehn surgery on a knot $K$ in $S^3$ is exceptional if it produces a reducible, toroidal or Seifert fibred manifold. It is known that a large arborescent knot admits no such surgery unless it is a type II arborescent knot. The main theorem of this paper shows that up to isotopy there are exactly three large arborescen…

A classification is given of the exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is determined as Lie algebra. In the present article, we give a pair of commuting involutive automorphisms…

We show that there are no tight nonholomorphic maps from irreducible domains into exceptional codomains, the only exception being the already known tight nonholomorphic maps from the Poincare disc. This follows up on previous work by the first author where this was shown for classical codomains.

Unified framework for exceptional and generalised geometry, and Poisson-Lie duality.

We prove two conjectures of C. Gordon. We show that the maximal number of exceptional Dehn surgeries on a 1-cusped hyperbolic 3-manifold is 10, and that the maximal intersection number between exceptional slopes is 8. The proof uses a combination of new geometric techniques and a rigorous computer-assisted calculation.

Classifies totally geodesic submanifolds in exceptional symmetric spaces.

Explains exceptional surgeries connecting maps and knot orbifolds.

We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a 3-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman and Watson, and also gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.

We survey aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence we show that if a hyperbolic knot $β$ in a compact, orientable, hyperbolic 3-manifold $M$ has the property that winding number and wrapping nu…