Related papers: Singularities of projected immersions revisited
For any compact Lie group $G$ and any $n$ we construct a smooth $G$-manifold $U_n(G)$ such that any smooth $n$-dimensional $G$-manifold can be embedded in $U_n(G)$ with a trivial normal bundle. Furthermore, we show that such embeddings are…
About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed…
We prove that a sequence of possibly branched, weak immersions of the two-sphere $S^2$ into an arbitrary compact riemannian manifold $(M^m,h)$ with uniformly bounded area and uniformly bounded $L^2-$norm of the second fundamental form…
A real Bott manifold is the total space of iterated RP^1 bundles starting with a point, where each RP^1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their…
In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented. This…
Given a sample of an abstract manifold immersed in some Euclidean space, we describe a way to recover the singular homology of the original manifold. It consists in estimating its tangent bundle -- seen as subset of another Euclidean space…
We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositions we turn these cobordisms into a sequence of embedded…
In this paper, we first construct $k$-dimensional compact complex manifolds from automorphisms of $\mathbb{C}^k$ which admit a fixed attracting point at infinity. Then, we charactize the fundamental group as well as the universal covering…
In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, we…
We introduce a new cohomology-theoretic method for classifying generic immersed curves in closed compact surfaces by using Gauss codes. This subsumes a result of J.S. Carter on classifying immersed curves in oriented compact surfaces, and…
Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…
The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional…
In this paper, we provide two different resolutions of structural sheaves of projectivized tangent bundles of smooth complete intersections. These resolutions allow in particular to obtain convenient (and completely explicit) descriptions…
Let S be a compact connected oriented orbifold surface We show that using Bers simultaneous uniformization, the moduli space of projective structure on S can be mapped biholomorphically onto the total space of the holomorphic cotangent…
We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results of Hofer-Lizan-Sikorav and Ivashkovich-Shevchishin to…
We classify immersions $f$ of $S^1$ in a $2$-manifold $M$ in terms of elementary invariants: the parity $S(f)$ of the number of double points of a self-transverse $C^1$-approximation of $f$, and the turning number $T(e\bar f)$ of the…
For a fixed closed manifold $P$, we construct a cobordism category of embedded manifolds with a single Baas-Sullivan singularity of type $P$. Our main theorem identifies the homotopy type of the classifying space of this cobordism category…
In this short note, we establish a quantitative description of the genericity of transversality of $C^1$-submanifolds in $\mathbb{R}^n$: Let $\Sigma \subset \mathbb{R}^n$ be a $d$-dimensional $C^1$-embedded submanifold where $n \geq d+1$.…
The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…
Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh. In this article we extend the results of arXiv:1609.05630 on the topology of real Bott manifolds to generalized real Bott manifolds. We…