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

We prove a conjecture of Shafarevich about universal coverings of projective manifolds provided the fundamental group is residually finite.

In this paper we show that the fibered isomorphism conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for the fundamental groups of a large class of complex manifolds. A consequence of this…

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.

Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental isomorphism functor holds for all additive functors, like K-theory, cyclic homology,…

We verify Katzarkov-Kontsevich-Pantev conjecture for Landau-Ginzburg models of smooth Fano threefolds.

In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

In this note, we prove the K- and L-theoretic Farrell-Jones Conjecture with coefficients in an additive category for fundamental groups of graphs of virtually cyclic groups.

We show that the Farrell-Jones Conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag-Solitar groups.

We prove Simon's conjecture for 3-manifolds.

This article generalises to K\"ahler orbifolds general results on uniformisation of compact K\"ahler manifolds such as the Shafarevich conjecture for linear fundamental groups.

In this paper, we focus on Oliver's $p$-group conjecture. We use elementary method to prove that Oliver's $p$-group conjecture holds for Sylow $p$-subgroups of unitary groups.

We prove Bloch's conjecture for numerical Campedelli surfaces with fundamental group of order $9$.

We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.

We prove that any Hamiltonian bundle whose fiber is a nilmanifold c-splits.

We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.

This paper initiates the study of circular orderability of $3$-manifold groups, motivated by the L-space conjecture. We show that a compact, connected, $\mathbb{P}^2$-irreducible $3$-manifold has a circularly orderable fundamental group if…

In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such generalized Bump-Hoffstein conjecture by proving some special…

We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric…