Simply connected space ≈ Simply connected space
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An analytical and numerical study of steady patches in the disc Open
We prove the existence of [math] -fold rotating patches for the Euler equations in the disc, for the simply connected and doubly connected cases. Compared to the planar case, the rigid boundary introduces rich dynamics for the lowest symme…
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On low-dimensional solvmanifolds Open
A nilmanifold resp. solvmanifold is a compact homogeneous space of a connected and simply-connected nilpotent resp. solvable Lie group by a lattice, i.e. a discrete co-compact subgroup. There is an easy criterion for nilpotent Lie groups w…
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ON BOUNDED-TYPE THIN LOCAL SETS OF THE TWO-DIMENSIONAL GAUSSIAN FREE FIELD Open
We study certain classes of local sets of the two-dimensional Gaussian free field (GFF) in a simply connected domain, and their relation to the conformal loop ensemble $\text{CLE}_{4}$ and its variants. More specifically, we consider bound…
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Liouville hypersurfaces and connect sum cobordisms Open
The purpose of this paper is to introduce Liouville hypersurfaces in contact manifolds, which generalize ribbons of Legendrian graphs and pages of supporting open books. Liouville hypersurfaces are used to define a gluing operation for con…
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A note on cobordisms of algebraic knots Open
We use Heegaard Floer homology to study smooth cobordisms of algebraic knots and complex deformations of cusp singularities of curves. The main tool will be the concordance invariant [math] : we study its behaviour with respect to connecte…
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On the boundaries of highly connected, almost closed manifolds Open
on the boundaries of highly connected, almost closed manifolds 213 freely use the language of ∞-categories as set out in [61], [62].In particular, all limits and colimits are taken in the homotopy invariant sense of [61]. AcknowledgmentsWe…
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Highly connected 7-manifolds and non-negative sectional curvature Open
In this article, a six-parameter family of highly connected 7-manifolds which admit an \nS \nO \n( \n3 \n) \n-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In partic…
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Compact Lie groups: Euler constructions and generalized Dyson conjecture Open
A generalized Euler parameterization of a compact Lie group is a way for parameterizing the group starting from a maximal Lie subgroup, which allows a simple characterization of the range of parameters. In the present paper we consider the…
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Stein fillings of contact 3-manifolds obtained as Legendrian surgeries Open
Stein fillings of contact 3-manifolds obtained as Legendrian surgeriesAmey Kaloti and
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Line bundles on rigid spaces in the<i>v</i>-topology Open
For a smooth rigid space X over a perfectoid field extension K of $\mathbb {Q}_p$ , we investigate how the v -Picard group of the associated diamond $X^{\diamondsuit }$ differs from the analytic Picard group of X . To this end, we construc…
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Complete noncompact G2-manifolds from asymptotically conical Calabi–Yau 3-folds Open
We develop a powerful new analytic method to construct complete non-compact G2-manifolds, i.e. Riemannian 7-manifolds (M,g) whose holonomy group is the compact exceptional Lie group G2. Our construction starts with a complete non-compact a…
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Infinitely many new families of complete cohomogeneity one G$_2$-manifolds: G$_2$ analogues of the Taub–NUT and Eguchi–Hanson spaces Open
We construct infinitely many new 1-parameter families of simply connected complete non-compact G _2 -manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geome…
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Simple crystallizations of 4-manifolds Open
Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We …
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EXISTENCE OF COMPATIBLE CONTACT STRUCTURES ON G(2)-MANIFOLDS Open
In this paper, we show the existence of (co-oriented) contact structures on certain classes of G(2)-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure (…
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On the classification of 1-connected 7-manifolds with torsion free second homology Open
We generalize a result of the author about the classification of 1-connected 7-manifolds and demonstrate its use by two concrete applications, one to 2-connected 7-manifolds (a new proof -- and slightly different formulation -- of an up to…
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Cohomogeneity one topological manifolds revisited Open
We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply-connected cohomogeneity one topological m…
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A model for configuration spaces of points Open
We construct a real combinatorial model for the configuration spaces of points of compact smooth oriented manifolds without boundary. We use these models to show that the real homotopy type of configuration spaces of a simply connected suc…
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Singular spaces with trivial canonical class Open
The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, and irreducible, simply-connected C…
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Semi-local simple connectedness of non-collapsing Ricci limit spaces Open
Let X be a non-collapsing Ricci limit space and let x\in X . We show that for any \epsilon>0 , there is r>0 such that every loop in B_t(x) is contractible in B_{(1+\epsilon)t}(x) , where t\in(0,r] . In particular, X is semi-locally simply …
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Tits geometry and positive curvature Open
There is a well-known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns–Spatzier provides a link between irreducible symmetric spaces of …
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The rational homotopy type of (n−1)‐connected manifolds of dimension up to 5n−3 Open
We define the Bianchi-Massey tensor of a topological space X to be a linear\nmap from a subquotient of the fourth tensor power of H*(X). We then prove that\nif M is a closed (n-1)-connected manifold of dimension at most 5n-3 (and n > 1)\nt…
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Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties Open
We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to characterizing incomplete, simply-connected, Riemannian manifo…
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$C^{\infty}$-logarithmic transformations and generalized complex structures Open
We show that there are generalized complex structures on all 4manifolds obtained by logarithmic transformations with arbitrary multiplicity along symplectic tori with trivial normal bundle.Applying a technique of broken Lefschetz fibration…
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Isotopy of the Dehn twist on K3 # K3 after asingle stabilization Open
Isotopy of the Dehn twist on K 3 # K 3 after a single stabilization
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On Mirror Maps for Manifolds of Exceptional Holonomy Open
We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups G2 and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to twist…
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On τ-tilting finite simply connected algebras Open
We show that $\\tau$-tilting finite simply connected algebras are\nrepresentation-finite. Then, some related algebras are considered, including\niterated tilted algebras, tubular algebras and so on. We also prove that the\n$\\tau$-tilting …
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds Open
Let M be a smooth compact and simply-connected manifold with simply-connected boundary $$\partial M$$ , r be a fixed odd natural number. We consider f, a $$C^1$$ self-map of M, preserving $$\partial M$$ . Under the assumption that the dime…
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Rational points and zero-cycles on rationally connected varieties over number fields Open
We report on progress in the qualitative study of rational points on rationally connected varieties over number fields, also examining integral points, zero-cycles, and non-rationally connected varieties. One of the main objectives is to h…
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Symmetric union presentations for 2-bridge ribbon knots Open
We prove that all 2-bridge ribbon knots are symmetric unions.
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Explicit fold maps on 7-dimensional closed and simply-connected manifolds of new classes Open
Closed (and simply-connected) manifolds whose dimensions are larger than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed manif…