Related papers: One-relator Sasakian groups

Given a compact, connected Lie group $K$, we use principal $K$-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let $M$ be a compact, connected, smooth manifold which supports an almost free…

We establish that, given $\Sigma$ a compact orientable surface, and $G$ a finitely presented one-ended group, the set of copies of $G$ in the mapping class group $\mathcal{MCG}(\Sigma)$ consisting of only pseudo-anosov elements except…

We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of…

We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known…

If $G$ is a finite primitive complex reflection group, all reflection subgroups of $G$ and their inclusions are determined up to conjugacy. As a consequence, it is shown that if the rank of $G$ is $n$ and if $G$ can be generated by $n$…

We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that for every finitely-presented group G there is a complex projective surface S with simple normal…

We obtain restrictions on the topology of a closed connected manifold B that bounds a (possibly noncompact) manifold whose interior V admits a complete Riemannian metric of nonpositive sectional curvature. If G denotes the fundamental group…

For a $2n+1$-dimensional compact Sasakian manifold, if $n\ge 2$, we prove that the analytic germ of the variety of representations of the fundamental group at every semi-simple representation is quadratic. To prove this result, we prove the…

Let G be an abelian group. For a subset A of G, Cyc(A) denotes the set of all elements x of G such that the cyclic subgroup generated by x is contained in A, and G is said to have the small subgroup generating property (abbreviated to SSGP)…

It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has an almost nilpotent fundamental group. Leftover questions and conjectures have asked if in this context the fundamental group is…

The main purpose of this paper is to provide a description of the fundamental group of a symplectic manifold in terms of Floer theoretic objects. As an application, we show that when counted with a suitable notion of multiplicity, non…

Let $X$ be a compact Riemann surface of genus $g\geq 2$, and let $G$ be a subgroup of $Aut(X)$. We show that if the Sylow $2$-subgroups of $G$ are cyclic, then $|G|\leq 30(g-1)$. If all Sylow subgroups of $G$ are cyclic, then, with two…

A finite group $G$ is called *uniformly generated*, if whenever there is a (strictly ascending) chain of subgroups $1<\langle x_1\rangle<\langle x_1,x_2\rangle <\cdots<\langle x_1,x_2,\dots,x_d\rangle=G$, then $d$ is the minimal number of…

A group $G$ is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of $G$ remain non-conjugate in some finite quotient of $G$. We prove that free groups and the fundamental…

We show that the fundamental group of any smooth subelliptic variety is finite. Moreover, it is also proved that every finite group can be realized as the fundamental group of a smooth subelliptic variety. As a consequence, it follows that…

We study fundamental groups of compact Sasaki manifolds and show that compared to K\"ahler groups, they exhibit rather different behaviour. This class of groups is not closed under taking direct products, and there is often an upper bound…

A class of one-relator groups such that every group in the class is determined by a triple of integers and is an HNN-extension of some Baumslag -- Solitar group is considered. A criterion for two groups in this class to be isomorphic and…

It is well-known that any isotopically connected diffeomorphism group $G$ of a manifold determines uniquely a singular foliation $\F_G$. A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism…

A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain K\"ahler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures…

We generalise a key result of one-relator group theory, namely Magnus's Freiheitssatz, to partially commutative groups, under sufficiently strong conditions on the relator. The main theorem shows that under our conditions, on an element $r$…