Related papers: The Lalonde-McDuff conjecture and the fundamental …

A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective…

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

The simple loop conjecture for 3-manifolds states that every 2-sided immersion of a closed surface into a 3-manifold is either injective on fundamental groups or admits a compression. This can be viewed as a generalization of the Loop…

In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…

We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.

We show that the Fibered Isomorphism Conjecture (FIC) of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for the fundamental groups of a large class of 3-manifolds. We also prove that if the FIC is…

We undertake a systematic investigation of compact aspherical manifolds with boundary; motivated by the plethora of examples in the bounded case and by the beauty of the theory in the closed case. Our main theorems give a homological…

We describe all abelian groups which can appear as the fundamental groups of closed symplectically aspherical manifolds. The proofs use the theory of symplectic Lefschetz fibrations.

Let $\Pi$ be the fundamental group of a smooth variety X over $F_p$. Given a non-Archimedean place $\lambda$ of the field of algebraic numbers which is prime to p, consider the $\lambda$-adic pro-semisimple completion of $\Pi$ as an object…

In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower…

Based on results by S.K. Roushon (math.KT/0408243 and math.KT/0405211) this thesis summarizes in an axiomatic way when a Meta-Isomorphism-Conjecture in the sense of Lueck and Reich (math.KT/0402405) is true for fundamental groups of…

We survey recent developments which led to the proof of the Benson-Gordon conjecture on K\"ahler quotients of solvable Lie groups. In addition we prove that the Albanese morphism of a K\"ahler manifold which is a homotopy torus is a…

We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

We prove that the universal covering space of a complex projective manifold is holomorphically convex provided its fundamental group is linear.

The ``Flux conjecture'' for symplectic manifolds states that the group of Hamiltonian diffeomorphisms is C^1-closed in the group of all symplectic diffeomorphisms. We prove the conjecture for spherically rational manifolds and for those…

This is the first of three articles on the Fibered Isomorphism Conjecture of Farrell and Jones for L-theory. We apply the general techniques developed in [15] and [16] to the L-theory case of the conjecture and prove several results. Here…

The main result of this paper is the proof for elliptic modular threefolds of conjectures on the existence and structure of a filtration on the Chow groups of smooth projective varieties. In the form we prove them these conjectures were…

In this note we prove the Weinstein conjecture for a class of symplectic manifolds including the uniruled manifolds based on Liu-Tian's result.

We prove Cherlin's conjecture, concerning binary primitive permutation groups, for those groups with socle isomorphic to a sporadic simple group.