Related papers: L^2-Invariants of Finite Aspherical CW-Complexes

We prove the No Invariant Line Fields conjecture for a class of generalized postcritically-finite branched covers on higher-dimensional Riemannian manifolds. Moreover, we establish a quasisymmetric uniformization theorem for this class of…

In this paper, we show that ``$L$-complete null hypersurfaces'' (i.e. ruled hypersurfaces foliated by entirety of light-like lines) as wave fronts in the $(n+1)$-dimensional Lorentz-Minkowski space are canonically induced by hypersurfaces…

In this paper we prove the Cheeger-M\"{u}ller theorem for $L^2$-analytic torsion form under the assumption that there exists a fiberwise Morse function and the Novikov-Shubin invariant is positive.

Consider the conjugation action of the general linear group $\operatorname{GL}_{2}(K)$ on the polynomial ring $K[X_{2 \times 2}]$. When $K$ is an infinite field, the ring of invariants is a polynomial ring generated by the trace and the…

Let X be as smooth complex projective variety with Neron-Severi group isomorphic to Z, and D an irreducible divisor with normal crossing singularities. Assume r is equal to 2 or 3. We prove that if the fundamental group of X doesn't have…

Let $X$ be a smooth projective variety acted on by a reductive group $G$. Let $L$ be a positive $G$-equivariant line bundle over $X$. We use the Witten deformation of the Dolbeault complex of $L$ to show, that the cohomology of the sheaf of…

A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of 'forbidden patterns', to be strongly aperiodic if all point…

The main result of this paper is the $G$-homotopy invariance of the $G$-index of signature operator of proper co-compact $G$-manifolds. If proper co-compact $G$ manifolds $X$ and $Y$ are $G$-homotopy equivalent, then we prove that the…

Let $F$ be a finite extension of $\mathbb{Q}_p$. The so-called supersingular representations are the basic building blocks in the theory of mod $p$ representations of ${\rm GL}_2(F)$. The space of pro-$p$-Iwahori invariants of a universal…

Let k be a field, and let {\pi}:\tilde{X} -> X be a proper birational morphism of irreducible k-varieties, where \tilde{X} is smooth and X has at worst quotient singularities. When the characteristic of k is zero, a theorem of Koll\'ar in…

There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…

Without using the $p$-adic Langlands correspondence, we prove that for many finite length smooth representations of $\mathrm{GL}_2(\mathbf{Q}_p)$ on $p$-torsion modules the $\mathrm{GL}_2(\mathbf{Q}_p)$-linear morphisms coincide with the…

The Slodowy slice is a flat Poisson deformation of its nilpotent part, and it was demonstrated by Lehn-Namikawa-Sorger that there is an interesting infinite family of nilpotent orbits in symplectic Lie algebras for which the slice is not…

Let $p\geq 5$ be a prime, and $\mathfrak{p}$ a prime of $\bar{\mathbb{Q}}$ above $p$. Let $g_1$ and $g_2$ be $\mathfrak{p}$-ordinary, $\mathfrak{p}$-distinguished and $p$-stabilized cuspidal newforms of nebentype characters $\epsilon_1,…

In this paper we extend Efimov's Theorem by proving that any complete surface in $\mathbb{R}^3$ with Gauss curvature bounded above by a negative constant outside a compact set has finite total curvature, finite area and is properly…

We prove that in closed almost complex manifolds of any dimension, generic perturbations of the almost complex structure suffice to achieve transversality for all unbranched multiple covers of simple pseudoholomorphic curves with…

In this paper we prove that the universal cover of a smooth projective variety with nilpotent fundamental group is holomorphically convex.

We study the deformation theory of nearly $\mathrm{G}_2$ manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly $\mathrm{G}_2$ structures are obstructed in…

For a banded link $L$ in a surface times a circle, the Witten-Reshetikhin-Turaev invariants are topological invariants depending on a sequence of complex $2p$-th roots of unity $(A_p)_{p\in 2\mathbb{N}}$. We show that there exists a…

Let $k$ be a field of characteristic zero and $G$ a finite group. We prove that for all $n\geq 2$, the $n$th Amitsur group is a stable $G$-birational invariant of smooth projective $G$-varieties over $k$. This was previously known for…