相关论文: A new orbit closure in genus 8?

We describe the 8-dimensional Wolf spaces as cohomogeneity one SU(3)-manifolds, and discover perturbations of the quaternion-kaehler metric on the simply-connected 8-manifold G_2/SO(4) that carry a closed fundamental 4-form but are not…

We introduce new polynomial isotopy invariants for closed braids. They are constructed as polynomial valued {\em Gauss diagram 1-cocycles} evaluated on the full rotation of the closed braid $\hat \beta$ around the core of the corresponding…

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is…

This paper is about topological rigidity of diagonal group actions on the homogeneous $\SL_4\big(\F(\!(t^{-1})\!)\big)/\SL_4(\F[t])$ where $\F$ is a finite field of characteristic $3$. We show that there is a non-closed relatively compact…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

We give a method for obtaining infinitely many framed knots which represent a diffeomorphic 4-manifold. We also study a relationship between the $n$-shake genus and the 4-ball genus of a knot. Furthermore we give a construction of homotopy…

We show that every GL(2, R) orbit closure of translation surfaces is either a connected component of a stratum, the hyperelliptic locus, or consists entirely of surfaces whose Jacobians have extra endomorphisms. We use this result to give…

We prove that there exists at least one close orbit in a given contact hypersurface in some symplectic manifolds.

Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence that this vertex set has 92 487 256 triangulations, partitioned into 247 451 symmetry classes.

The nonorientable four-ball genus of a knot $K$ in $S^3$ is the minimal first Betti number of nonorientable surfaces in $B^4$ bounded by $K$. By amalgamating ideas from involutive knot Floer homology and unoriented knot Floer homology, we…

Four-dimensional supergravity theories are reinterpreted in a 12-dimensional F-theory framework. The O(8) symmetry of N=8 supergravity is related to a reduction of F-theory on T_8, with the seventy scalars formally associated, by O(8)…

In this note we give an example of a one-dimensional manifold with two connected components and a complete metric whose group of isometries has an orbit which is not closed. This answers a question of S. Gao and A. S. Kechris.

This paper presents evidence supporting the surprising conjecture that in the topological category the slice genus of a satellite knot $P(K)$ is bounded above by the sum of the slice genera of $K$ and $P(U)$. Our main result establishes…

We prove that if the order of the first homology of the 2-fold branched cover of a knot K in the 3-sphere is given by pm where p is a prime congruent to 3 mod 4 and gcd(p,m) =1, then K is of infinite order in the knot concordance group.…

In the complement of a hyperbolic Montesinos knot with 4 rational tangles, we investigate the number of closed, connected, essential, orientable surfaces of a fixed genus $g$, up to isotopy. We show that there are exactly 12 genus 2…

Over the course of the past two decades, observational surveys have unveiled the intricate orbital structure of the Kuiper Belt, a field of icy bodies orbiting the Sun beyond Neptune. In addition to a host of readily-predictable orbital…

This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Cohomologies of wrap groups…

We prove some classification results for tight contact structure in the 3-space, -ball and -sphere that are invariant with respect to some arbitrary involution, that is conjugated to the standard rotation around the x-axis. Unlike the…

We describe a new class of supersymmetric orientifolds which combine the world-sheet parity transformation with a complex conjugation in the compact directions. As an example, we investigate in detail the orientifold of the Z_3 toroidal…

In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying the construction of knot Floer homology HFK-minus. The resulting groups were then used to define concordance homomorphisms indexed by t in…