相关论文: An explicit formula for a branched covering from $…

We present an exact formula for the number of distinct crease patterns in a square shaped region of a given size that appear in the 2 dimensional paperfolding structure.

We show that every closed connected non-orientable PL $4$-manifold $X$ is a simple branched covering of $\RP^4$. We also show that $X$ is a simple branched covering of the twisted $S^3$-bundle $S^1 \simtimes S^3$ if and only if the first…

In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…

Branch points of a real 2-surface S in a 4-manifold M generalize the branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces. We investigate such a branch point p when S is…

We describe the topology of a general polynomial mapping $f:\Bbb C^2\to\Bbb C^2.$

Starting with an O(2)-principal fibration over a closed oriented surface F_g, g>=1, a 2-fold covering of the total space is said to be special when the monodromy sends the fiber SO(2) = S^1 to the nontrivial element of Z_2. Adapting D…

In this paper we find an explicit formula for the number of topologically different ramified coverings $C\to\CP^1$ (C is a compact Riemann surface of genus g) with only one complicated branching point in terms of Hodge integrals over the…

We construct a sofic approximation of $\mathbb F_2\times\mathbb F_2$ that is not essentially a "branched cover" of a sofic approximation by homomorphisms. This answers a question of L. Bowen.

We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U(N). The model solves the general…

We construct a family of smooth branched coverings of degree $2$ of the sphere $S^2$ having a completely invariant indecomposable continuum $K$ and infinitely many Wada Lakes.

Square-tiled surfaces can be classified by their number of squares and their cylinder diagrams (also called realizable separatrix diagrams). For the case of $n$ squares and two cone points with angle $4 \pi$ each, we set up and parametrize…

We compute the supersymmetric partition function of an $\mathcal{N}=1$ chiral multiplet coupled to an external Abelian gauge field on complex manifolds with $T^2 \times S^2$ topology. The result is locally holomorphic in the complex…

We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of…

We give sharp sectional curvature estimates for complete immersed cylindrically bounded $m$-submanifolds $\phi:M\to N\times\mathbb{R}^{\ell}$, $n+\ell\leq 2m-1$ provided that either $\phi$ is proper with the second fundamental form with…

We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two…

We prove that the double branched cover of a twist-roll spun knot in $S^4$ is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun knot connected sum with a trivial projective plane is…

We provide homological foundations to establish conjectural homological projective dualities between 1) S^2 P^3 and the double cover of the projective 9-space branched along the symmetric determinantal quartic, and 2) S^2 P^4 and the double…

We investigate the topology of a double cover of a complex affine plane branching along a nodal real line arrangement. We define certain topological 2-cycles in the double plane using the real structure of the arrangement, and calculate…

We prove that one can cover the $1 \times b$ rectangle by equal squares on both sides in one layer iff $b = p \pm \sqrt{p^2 - r^2} $, where $p \ge r \ge 0$ and $p,q \in \mathbb{Q}$.

We present an explicit branching formula for the six-parameter Macdonald-Koornwinder polynomials with hyperoctahedral symmetry.