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Open AccessTrisecting a 4-dimensional book into three chapters
We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algor...
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Article
Open AccessProjectively induced Kähler cones over regular Sasakian manifolds
Motivated by a conjecture in Loi et al. (Math Zeit 290:599–613, 2018) we prove that the Kähler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. W...
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Open AccessTop degree \(\ell ^p\) -homology and conformal dimension of buildings
For a non-compact finite thickness building whose Davis apartment is an orientable pseudomanifold, we compute the supremum of the set of $$p>1...
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Open AccessFundamental groups and group presentations with bounded relator lengths
We study the geometry of compact geodesic spaces with trivial first Betti number admitting large finite groups of isometries. We show that if a finite group G acts by isometries on a compact geodesic space X whos...
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Article
Open AccessThe Liouville current of holomorphic quadratic differential metrics
In this paper we study the Liouville current of flat cone metrics coming from a holomorphic quadratic differential. Anja Bankovic and Christopher J. Leininger proved in Bankovic and Leininger (Trans Am Math So...
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Open AccessTemperedness of locally symmetric spaces: the product case
Let \(X=X_1\times X_2\) X = ...
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Open AccessDistribution of periodic orbits in the homology group of a knot complement
Consider a transitive Anosov flow on a closed 3-manifold. After removing a finite set of null-homologous periodic orbits, we study the distribution of the remaining periodic orbits in the homology of the knot ...
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Open AccessTrisections obtained by trivially regluing surface-knots
Let S be a \(P^2\) P 2 ...
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Open AccessPrym representations of the handlebody group
Let S be an oriented, closed surface of genus g. The map** class group of S is the group of orientation preserving homeomorphisms of S modulo isotopy. In 1997, Looijenga introduced the Prym representations, whi...
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Open AccessK3 surfaces with two involutions and low Picard number
Let X be a complex algebraic K3 surface of degree 2d and with Picard number \(\rho \) ρ ...
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Open AccessLeft-invariant distributions diffeomorphic to flat distributions
For a stratified group G, we construct a class of Lie groups endowed with a left-invariant distribution locally diffeomorphic to the flat distribution of G. Vice versa, we show that all Lie groups with a left-inv...
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Open AccessCurvature bounds on length-minimizing discs
We show that a length-minimizing disk inherits the upper curvature bound of the target. As a consequence we prove that harmonic discs and ruled discs inherit the upper curvature bound from the ambient space.
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Open AccessCusped Borel Anosov representations with positivity
We show that if a cusped Borel Anosov representation from a lattice \(\Gamma \subset \textsf{PGL}_2({{\,\mathrm{\mathbb {R}}\,}})\) ...
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Open AccessComplete Calabi–Yau metrics from smoothing Calabi–Yau complete intersections
We construct complete Calabi–Yau metrics on non-compact manifolds that are smoothings of an initial complete intersection \(V_0\) ...
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Open AccessUnique continuation problem on RCD Spaces. I
In this note we establish the weak unique continuation theorem for caloric functions on compact RCD(K, 2) spaces and show that there exists an RCD(K, 4) space on which there exist non-trivial eigenfunctions of th...
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Open AccessCoregularity of Fano varieties
The absolute regularity of a Fano variety, denoted by \(\hat{\textrm{reg}}(X)\) ...
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Open AccessTopological and dynamical properties of Torelli groups of partitioned surfaces
Putman introduced a notion of a partitioned surface which is a surface with boundary with decoration restricting how the surface can be embedded into larger surfaces, and defined the Torelli group of the parti...
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Open AccessCircumcenter extension maps for non-positively curved spaces
We show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a map, called circumcenter extension, provided that the manifolds satisfy certain visibility conditio...
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Open AccessHomotopy equivalent boundaries of cube complexes
A finite-dimensional CAT(0) cube complex X is equipped with several well-studied boundaries. These include the Tits boundary \(\partial _TX\) ...
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Open AccessMedian quasimorphisms on \({{\,\mathrm{{CAT}}\,}}(0)\) cube complexes and their cup products
Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms,...
