Cross-cap singularities counted with sign

2015/06/16 by Iwona Krzyżanowska, Krzyżanowska, Iwona · 1 citation
Computer Science · Engineering · Mathematics · #12Y05 #14P25 #57R42 #57R45 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1506.04873

openalex publication_date 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There is presented a method for computing the algebraic number of cross-cap singularities for mapping from m dimensional compact manifold with boundary M into R^(2m-1), m is odd. As an application, the intersection number of an immersion g from (m-1)-dimensional sphere to R^(2m-2) is described as the algebraic number of cross-caps of a mapping naturally associated with g.

Citations

• The general type of singularity of a set of 2n−1 smooth functions of n variables

Cited by

• Mappings into the Stiefel manifold and cross-cap singularities

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