Topological Methods in Nonlinear Analysis

Functions and vector fields on $C(\mathbb{C}P^n)$-singular manifolds

Alice K.M. Libardi and Vladimir V. Sharko

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Abstract

In this paper we study functions and vector fields with isolated singularities on a $C(\mathbb{C}P^n)$-singular manifold. In general, a $C(\mathbb{C}P^n)$-singular manifold is obtained from a smooth $(2n+1)$-manifold with boundary which is a disjoint union of complex projective spaces $\mathbb{C}P^n \cup\ldots \cup\mathbb{C}P^n$ and subsequent capture of the cone over each component $\mathbb{C}P^n$ of the boundary. We calculate the Euler characteristic of a compact $C(\mathbb{C}P^n)$-singular manifold $M^{2n+1}$ with finite isolated singular points. We also prove a version of the Poincaré-Hopf Index Theorem for an almost smooth vector field with finite number of zeros on a $C(\mathbb{C}P^n)$-singular manifold.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 2 (2015), 697-715.

Dates
First available in Project Euclid: 21 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1458588657

Digital Object Identifier
doi:10.12775/TMNA.2015.081

Mathematical Reviews number (MathSciNet)
MR3273973

Zentralblatt MATH identifier
1365.57034

Citation

Libardi, Alice K.M.; Sharko, Vladimir V. Functions and vector fields on $C(\mathbb{C}P^n)$-singular manifolds. Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 697--715. doi:10.12775/TMNA.2015.081. https://projecteuclid.org/euclid.tmna/1458588657


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