The pro-Chern-Schwarz-MacPherson class in Borel-Moore motivic homology
Fangzhou Jin, Peng Sun, Enlin Yang
TL;DR
This paper demonstrates the equivalence of the zero-dimensional pro-Chern-Schwarz-MacPherson class with the pro-characteristic class in Borel-Moore motivic homology and introduces a quadratic refinement in Milnor-Witt homology.
Contribution
It establishes a new connection between pro-Chern-Schwarz-MacPherson classes and Borel-Moore motivic homology, including a quadratic refinement in Milnor-Witt homology.
Findings
Zero-dimensional pro-Chern-Schwarz-MacPherson class equals pro-characteristic class in Borel-Moore motivic homology.
Construction of a quadratic refinement in Borel-Moore Milnor-Witt homology.
Abstract
We show that the zero-dimensional part of the pro-Chern-Schwarz-MacPherson class defined by Aluffi is equal to the pro-characteristic class in limit Borel-Moore motivic homology. A similar construction also produces a quadratic refinement of this class in the limit Borel-Moore Milnor-Witt homology.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Geometry and complex manifolds