arXiv subjects

Camila M. Ruiz

Publications and source records attributed to Camila M. Ruiz.

2 recordsLinked to original sources

arXiv2016

Morin singularities of coframes and frames

Inspired by the properties of an $n$-frame of gradients $(\nabla f_1, \ldots, \nabla f_n)$ of a Morin map $f:M\rightarrow\mathbb{R}^n$, with $\dim M\geq n$, we introduce the notion of Morin singularities in the context of singular $n$-coframes and singular $n$-frames. We also study the singularities of generic 1-forms associated to a Morin $n$-coframe, in order to generalize a result of T. Fukuda [4, Theorem 1], which establishes a modulo 2 congruence between the Euler characteristic of a compact manifold $M$ and the Euler characteristics of the singular sets of a Morin map defined on $M$, to the case of Morin $n$-coframes and Morin $n$-frames.

math.GT↗

arXiv2016

A new proof of a theorem of Dutertre and Fukui on Morin singularities

In [2], N.Dutertre and T. Fukui used Viro's integral calculus to study the topology of stable maps $f:M\rightarrow N$ between two smooth manifolds $M$ and $N$. They also discussed several applications to Morin maps. In particular, in Theorem 6.2 [2], they show an equality relating the Euler characteristic of a compact manifold $M$ and the Euler characteristic of the singular sets of a Morin map defined on $M$. In this paper we show how Morse theory for manifolds with boundary can be applied to the study of the singular sets of a Morin map in order to obtain a new proof of Dutertre-Fukui's Theorem when $N=\mathbb{R}^n$.

math.GT↗