@article{Libardi_Sharko_2015, title={Functions and Vector Fields on C(CP^n)-singular manifolds}, volume={46}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2015.081}, DOI={10.12775/TMNA.2015.081}, abstractNote={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 Poincare-Hopf Index Theorem for an almost smooth vector field with finite number of zeros on a~$C(\mathbb{C}P^n)$-singular manifold.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Libardi, Alice Kimie Miwa and Sharko, Vladimir V.}, year={2015}, month={Dec.}, pages={697–716} }