Cross-cap singularities counted with sign
Iwona Krzy\.zanowska

TL;DR
This paper introduces a method to compute the algebraic count of cross-cap singularities in mappings from odd-dimensional manifolds into Euclidean space, with applications to intersection numbers of immersions.
Contribution
It presents a novel approach for counting cross-cap singularities algebraically and relates this to intersection numbers of immersions, expanding understanding of singularity theory.
Findings
Method for computing algebraic number of cross-caps
Application to intersection number of sphere immersions
Provides a link between singularities and intersection theory
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Polynomial and algebraic computation · Advanced Numerical Analysis Techniques
