Cross-cap singularities counted with sign

• Published in: Algebra and Discrete Mathematics
• Date: 2018
• Main Author: Krzyzanowska, I.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188361
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Cross-cap singularities counted with sign / I. Krzyzanowska // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 2. — С. 257–268. — Бібліогр.: 11 назв. — англ.

A method for computing the algebraic number of cross-cap singularities for mapping from m-dimensional compact manifold with boundary M ⊂ Rᵐ into R²ᵐ⁻¹, m is odd, is presented. As an application, the intersection number of an immersion g : Sᵐ⁻¹ (r) → R²ᵐ⁻² is described as the algebraic number of cros...