Elimination of singularities of smooth mappings of 4-manifolds into 3-manifolds
英文摘要：
This paper has been withdrawn. Its new version has been published.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Regular homotopy classes of locally generic mappings
In this paper we generalize the notion of regular homotopy of immersions of a closed connected n-manifold into R^{2n-1} to locally generic mappings. The main result is that if n=2 then two mappings with singularities are regularly homotopic if and only if they have the same number of cross-cap (or Whitney-umbrella) singularities. As an application, we get a description of the path-components of the space of those immersions of a surface into R^4 whose projections into R^3 are locally generic.
math.ATmath.GT
Obstructions to the existence of fold maps
We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in terms of characteristic classes, which arise as Postnikov invariants, and can be interpreted as primary and secondary obstructions to the elimination of certain singularities. We also discuss the relationship between the existence problem of fold maps and that of vector fields of stabilized tangent bundles.
math.ATmath.GT
Vanishing cycles, plane curve singularities, and framed mapping class groups
Let f be an isolated plane curve singularity with Milnor fiber of genus at least 5. For all such f, we give (a) an intrinsic description of the geometric monodromy group that does not invoke the notion of the versal deformation space, and (b) an easy criterion to decide if a given simple closed curve in the Milnor fiber is a vanishing cycle or not. With the lone exception of singularities of type $A_n$ and $D_n$, we find that both are determined completely by a canonical framing of the Milnor fiber induced by the Hamiltonian vector field associated to f. As a corollary we answer a question of …
math.AGmath.GT
Singularities of quadratic differentials and extremal Teichmüller mappings defined by Dehn twists
Let $S$ be a Riemann surface of type $(p,n)$ with $3p-3+n>0$. Let $ω$ be a pseudo-Anosov map of $S$ that is obtained from Dehn twists along two families $\{A,B\}$ of simple closed geodesics that fill $S$. Then $ω$ can be realized as an extremal Teichmüller mapping on a surface of type $(p,n)$ which is also denoted by $S$. Let $ϕ$ be the corresponding holomorphic quadratic differential on $S$. In this paper, we compare the locations of some distinguished points on $S$ in the $ϕ$-flat metric to their locations with respect to the complete hyperbolic metric. More precisely, we show that all possi…
math.CVmath.GT
Functions with isolated singularities on surfaces
Let M be a smooth connected compact surface, P be either the real line R^1 or the circle S^1, and f:M-->P be a smooth mapping. In a previous series of papers for the case when f is a Morse map the author calculated the homotopy types of stabilizers and orbits of f with respect to the right action of the diffeomorphisms group of M. The present paper extends those calculations to a large class of maps M-->P with degenerate singularities satisfying certain set of axioms.
math.ATmath.GT
Tête-à-tête twists, monodromies and representation of elements of Mapping Class Group
We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: tête-à-tête graphs and twists. We completely characterize mapping classes that can be represented by tête-à-tête twists, and generalize the notion to be able to represent any class of the mapping class group relative to the boundary which is boundary-free periodic. This improves previous work on the subject by C. Graf. Furthermore, we introduce the class of mixed tête-à-tête graphs and twists, and prove that mixed tête-à-tête t…
math.GT
更多相关论文收起更多论文
Singularities of projected immersions revisited
Sz\H ucs proved in 2000 that the $r$-tuple-point manifold of a generic immersion is cobordant to the $Σ^{1_{r-1}}$-point manifold of its generic projection. Here we slightly extend this by showing that the natural mappings of these manifolds are bordant to each other. The main novelty of our approach is that we construct the bordism explicitly.
math.GT
On smooth foliations with Morse singularities
Let $M$ be a smooth manifold and let $\F$ be a codimension one, $C^\infty$ foliation on $M$, with isolated singularities of Morse type. The study and classification of pairs $(M,\F)$ is a challenging (and difficult) problem. In this setting, a classical result due to Reeb \cite{Reeb} states that a manifold admitting a foliation with exactly two center-type singularities is a sphere. In particular this is true if the foliation is given by a function. Along these lines a result due to Eells and Kuiper \cite{Ku-Ee} classify manifolds having a real-valued function admitting exactly three non-degen…
math.GT
二元正态混合中的奇点
Singularities in bivariate normal mixtures
本文利用映射奇点理论对二元正态密度映射进行分类，揭示三种类型及其几何性质，并给出各类混合众数数量的上界。
math.GTmath.STstat.TH
Elimination of cusps in dimension 4 and its applications
Several new combinatorial descriptions of closed 4-manifolds have recently been introduced in the study of smooth maps from 4-manifolds to surfaces. These descriptions consist of simple closed curves in a closed, orientable surface and these curves appear as so called vanishing sets of corresponding maps. In the present paper we focus on homotopies canceling pairs of cusps so called cusp merges. We first discuss the classification problem of such homotopies, showing that there is a one-to-one correspondence between the set of homotopy classes of cusp merges canceling a given pair of cusps and …
math.GT
加权奇点的单值微分同胚与Seiberg--Witten理论
The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory
本文证明加权齐次型二维孤立超曲面奇点（非有理二重点）的Milnor纤维单值微分同胚在光滑映射类群中具有无限阶，并借助等变Seiberg--Witten--Floer同调中的切触不变量类比，将该结果归结为负定向Seifert纤维化有理同调3-球面辛填充边界Dehn扭转的无限阶性质。
math.AGmath.GTmath.SG
The Chess conjecture
We prove that the homotopy class of a Morin mapping f: P^p --> Q^q with p-q odd contains a cusp mapping. This affirmatively solves a strengthened version of the Chess conjecture [DS Chess, A note on the classes [S_1^k(f)], Proc. Symp. Pure Math., 40 (1983) 221-224] and [VI Arnol'd, VA Vasil'ev, VV Goryunov, OV Lyashenko, Dynamical systems VI. Singularities, local and global theory, Encyclopedia of Mathematical Sciences - Vol. 6 (Springer, Berlin, 1993)]. Also, in view of the Saeki-Sakuma theorem [O Saeki, K Sakuma, Maps with only Morin singularities and the Hopf invariant one problem, Math. Pr…
math.GT
