Related papers: The L^1 Ehrenpreis Conjecture

Let $M$ and $N$ be two closed hyperbolic Riemann surfaces. The Ehrenpreis Conjecture (proved by Kahn-Markovic) asserts that for any $\epsilon>0$ there are finite covers $M_\epsilon \to M$, and $N_\epsilon \to N$, such that the Teichmuller…

We prove the following: 1. Let epsilon>0 and let S_1,S_2 be two closed hyperbolic surfaces. Then there exists locally-isometric covers S'_i of S_i (for i=1,2) such that there is a (1+\epsilon) bi-Lipschitz homeomorphism between S'_1 and…

The topology of the embedding of the coadjoint orbits of the unitary group U(H) of an in-finite dimensional complex Hilbert space H, as canonically determined subsets of the B-space T_s of symmetric trace class operators, is investigated.…

We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l>2 be prime and A a finite abelian l-group. Then there…

This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that \pi_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at…

We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces (the good pants are pairs of pants whose cuffs have the length nearly equal to some large number R). Combined with our…

Recently L. Nicolaescu and the author formulated a conjecture which relates the geometric genus of a complex analytic normal surface singularity (whose link $M$ is a rational homology sphere) with the Seiberg-Witten invariant of $M$…

The $L$-space conjecture asserts the equivalence, for prime 3-manifolds, of three properties: not being an $L$-space, having a left-orderable fundamental group, and admitting a co-oriented taut foliation. We investigate these properties for…

Let $S$ be a closed Shimura variety uniformized by the complex $n$-ball. The Hodge conjecture predicts that every Hodge class in $H^{2k} (S, \Q)$, $k=0, \ldots, n$, is algebraic. We show that this holds for all degree $k$ away from the…

We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian…

Morel's stable connectivity theorems state that for any connective $S^1$-spectrum $F$ of motivic spaces (Nisnevich simplicial sheaves) over an arbitrary field, the spectrum $L_{\mathbb A^1}(F)$ is connective, and the same property for…

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 show that whenever a closed symplectic manifold admits a Hamiltonian diffeomorphism with finitely many simple periodic orbits, the manifold has a spherical homology class of degree two with positive symplectic area and positive integral…

The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…

We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable…

The $L$-space conjecture asserts the equivalence, for prime $3$-manifolds, of three properties: not being an $L$-space ($NLS$), having a left-orderable fundamental group ($LO$), and admitting a co-orientable taut foliation ($CTF$). In this…

We show that the continuous \'etale cohomology groups $H^n_{\mathrm{cont}}(X,\mathbf{Z}_l(n))$ of smooth varieties $X$ over a finite field $k$ are spanned as $\mathbf{Z}_l$-modules by the $n$-th Milnor $K$-sheaf locally for the Zariski…

Let N \subseteq M be von Neumann algebras and E:M\to N a faithful normal conditional expectation. In this work it is shown that the similarity orbit S(E) of E by the natural action of the invertible group of G_M of M has a natural complex…

Let f: X -> Y be a separated morphism of schemes of finite type over a finite field of characteristic p, let Lambda be an artinian local Z_p-algebra with finite residue field, let m be the maximal ideal of Lambda, and let L^\bullet be a…

We prove that compact 3-manifolds $M$ of constant curvature +1 with boundary a minimal surface are locally naturally parametrized by the conformal class of the boundary metric $\gamma$ in the Teichmuller space of $\partial M$, when…