Related papers: Almost complex circle actions with few fixed point…

We prove that every action of $A_5$ on a finite $2$-dimensional contractible complex has a fixed point.

One central problem in real algebraic geometry is to classify the real structures of a given complex manifold. We address this problem for compact hyperk\"ahler manifolds by showing that any such manifold admits only finitely many real…

We give several explicit examples of compact manifolds with a $1$-parameter family of almost complex structures having arbitrarily small Nijenhuis tensor in the $C^0$-norm. The $4$-dimensional examples possess no complex structure, whereas…

Motivated by the theory of Riemann surfaces, we classify all possibilities for finite simple groups acting faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most three fixed…

In this note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is…

The aim of this paper is to study compact 5--manifolds which admit fixed point free circle actions. The first result implies that the torsion in the second homology and the second Stiefel--Whitney class have to satisfy strong restrictions.…

A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.

In this series of two articles, we prove that every action of a finite group $G$ on a finite and contractible $2$-complex has a fixed point. The proof goes by constructing a nontrivial representation of the fundamental group of each of the…

We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3-manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various…

It is proved that if an almost K\"ahler manifold of dimension greater or equal to 8 is of pointwise constant antiholomorphic sectional curvature, then it is a complex space form.

This article deals with 3-forms on 6-dimensional manifodls, the first dimension where the classification of 3-forms is not trivial. There are three classes of multisymplectic 3-forms there. We study the class which is closely related to…

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 record an answer to the question "In which dimensions is the connected sum of two closed almost complex manifolds necessarily an almost complex manifold?". In the process of doing so, we are naturally led to ask "For which values of l is…

We show that in dimension 8 the geography of symplectic manifolds does not differ from that of almost complex ones.

We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.

Let $M$ be a compact oriented simply-connected manifold of dimension at least 8. Assume $M$ is equipped with a torsion-free semi-free circle action with isolated fixed points. We prove $M$ has a perfect invariant Morse-Smale function. The…

Consider an effective Hamiltonian circle action on a compact symplectic $2n$-dimensional manifold $(M, \omega)$. Assume that the fixed set $M^{S^1}$ is {\em minimal}, in two senses: it has exactly two components, $X$ and $Y$, and $\dim(X) +…

We construct a finitely presented, infinite, simple group that acts by homeomorphisms on the circle, but does not admit a non-trivial action by $C^1$-diffeomorphisms on the circle. The group emerges as a group of piecewise projective…

We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: $\mathfrak{A}_5$, $\operatorname{PSL}_2(\mathbf{F}_7)$, $\mathfrak{A}_6$,…

In this paper we consider dynamical systems generated by $(3,2)$-rational functions on the field of $p$-adic complex numbers. Each such function has three fixed points. We show that Siegel disks of the dynamical system may either coincide…