Related papers: Normal Smoothings for Smooth Cube Manifolds
We prove that every piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly. This solves a…
We classify projective manifolds with flat holomorphic conformal structures.
We prove existence and stability of smooth entire strictly convex spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space. The proof is based on barrier constructions and local a priori estimates.
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
Tadao Oda conjectured that every smooth polytope has the Integer Decomposition Property. In this paper, we show this result for a subclass of polytopes: smooth combinatorial cubes of any dimension.
We prove that the stably free modules over a smooth affine threefold over an algebraically closed field of characteristic different from 2 are free.
Assuming the Riemann hypothesis we demonstrate the existence of smooth numbers in certain short intervals.
In this paper we discuss the notion of smoothness in complex algebraic supergeometry and we prove that all affine complex algebraic supergroups are smooth. We then prove the stabilizer theorem in the algebraic context, providing some useful…
The classical Theorem of Mumford states that a topologically regular complex algebraic surface in $\mathbb{C}^3$ with an isolated singular point is smooth. We proof that any Lipschitz regular complex algebraic set is smooth. No restriction…
In this paper, we give definitions and characterizations of normal and spherical curves in the dual space. We show that normal curves are also spherical curves in D^3.
In this paper we study smooth structures on closed oriented 4-manifolds with fundamental group Z_2 and definite intersection form. We construct infinitely many irreducible, smooth, oriented, closed, definite four-manifolds with fundamental…
We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$, and as a…
We discuss K3 surfaces in characteristic two that contain the Kummer configuration formed by smooth rational curves on it.
In this paper, we investigate the differential smoothness of graded skew Clifford algebras.
In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also…
We show that every 'conveniently Hoelder' homomorphism between Lie groups in the sense of convenient differential calculus is smooth (in the convenient sense). In particular, every Lip^0 homomorphism is smooth.
We give a comprehensive representation of the construction of dyadic cubes in spaces of homogeneous type.
We prove the existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds provided there are barriers.
Over a decade ago, it was shown that every edge unfolding of the Platonic solids was without self-overlap, yielding a valid net. We consider this property for regular polytopes in arbitrary dimensions, notably the simplex, cube, and…
We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann's construction [5].