Related papers: $\mathbb{Z}/2\mathbb{Z}$-Equivariant smoothings of…

We show that any compact surface of genus zero in Euclidean 3-space that satisfies a quasiconformal inequality between its principal curvatures is a round sphere. This solves an old open problem by H. Hopf, and gives a spherical version of…

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…

Working in characteristic two, I classify nonsmooth Enriques surfaces with normal crossing singularities. Using Kato's theory of logarithmic structures, I show that such surfaces are smoothable and lift to characteristic zero, provided they…

According to an old result of Sch\"utzenberger, the involutions in a given two-sided cell of the symmetric group $\SG_n$ are all conjugate. In this paper, we study possible generalisations of this property to other types of Coxeter groups.…

In this paper, we classify smooth 5-manifolds with fundamental group isomorphic to $\z/2$ and universal cover diffeomorphic to $S^2 \times S^3$. This gives a classification of smooth free involutions on $S^2 \times S^3$ up to conjugation.

Let X be a holomorphic symplectic fourfold such that b_2=23 and i a symplectic involution of X . The fixed locus F of i is a smooth symplectic submanifold of X; we show that F contains at least 12 isolated points and 1 smooth surface. We…

We investigate the realisability of the Casson-Sullivan invariant for homeomorphisms of smooth $4$-manifolds, which is the obstruction to a homeomorphism being stably pseudo-isotopic to a diffeomorphism, valued in the third cohomology of…

The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is…

Let $E$ be an elliptic curve with good ordinary reduction at an odd prime $p$. Assuming that Greenberg's $\mu=0$ conjecture holds, we show that the $\lambda$-invariants of the Mazur--Tate elements attached to $E$ either stabilise to the…

Let $(S,\omega)$ be a closed connected oriented surface whose genus $l$ is at least two equipped with a symplectic form. Then we show the vanishing of the cup product of the fluxes of commuting symplectomorphisms. This result may be…

Let $(S^2,\omega)$ be a symplectic sphere, and let $\tau \colon S^2 \to S^2$ be an anti-symplectic involution of $(S^2,\omega)$. We consider the product $(S^2,\omega) \times (S^2,\omega)$ endowed with the anti-symplectic involution $\tau…

It is a well known fact that every embedded symplectic surface $\Sigma$ in a symplectic 4-manifold $(X^4,\omega)$ can be made $J$-holomorphic for some almost-complex structure $J$ compatible with $\omega$. In this paper we investigate when…

We show that the space of anti-symplectic involutions of a monotone $S^2\times S^2$ whose fixed points set is a Lagrangian sphere is connected. This follows from a stronger result, namely that any two anti-symplectic involutions in that…

We consider the following problem: Under what assumptions do one or more of the following are equivalent for a ring $R$: (A) $R$ is Morita equivalent to a ring with involution, (B) $R$ is Morita equivalent to a ring with an…

Let $\mathcal{M}_{C}(2, 0)$ be the moduli space of semistable rank two and degree zero Higgs bundles on a smooth complex hyperelliptic curve $C$ of genus three. We prove that the quotient of $\mathcal{M}_{C}(2, 0)$ by a twisted version of…

In this article, we construct zeta morphisms for the universal deformations of odd absolutely irreducible two dimensional mod p Galois representations satisfying some mild assumptions, and prove that our zeta morphisms interpolate Kato's…

We investigate the necessary and sufficient condition for the existence of good involutions of symplectic quandles, which are defined on free $R$-modules with an antisymmetric bilinear form. In particular, we discuss the nonexistence of…

Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a classification of the pairs $(A,G)$ such that the quotient $A/G$…

We prove that every non-degenerate Reeb flow on a closed contact manifold $M$ admitting a strong symplectic filling $W$ with vanishing first Chern class carries at least two geometrically distinct closed orbits provided that the positive…

The holomorphy conjecture states roughly that Igusa's zeta function associated to a hypersurface and a character is holomorphic on $\mathbb{C}$ whenever the order of the character does not divide the order of any eigenvalue of the local…