2025/02/16 by Candace Bethea, Bethea, Candace, Kirsten Wickelgren +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2502.10964
openalex publication_date 2025/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the equivariant degree and local degree of a proper G-equivariant map between smooth G-manifolds when G is a compact Lie group and prove a local to global result. We show the local degree can be used to compute the equivariant Euler characteristic of a smooth, compact G-manifold and the Euler number of a relatively oriented G-equivariant vector bundle when G is finite. As an application, we give an equivariantly enriched count of rational plane cubics through a G-invariant set of 8 general points in ℂℙ2, valued in the representation ring and Burnside ring of a finite group. When ℤ/2 acts by pointwise complex conjugation this recovers a signed count of real rational cubics.