Comparing Euler classes
By A. Asok, Jean Fasel. 2013
53 citations recorded by the source corpus.
We establish the equality of two definitions of an Euler class in algebraic geometry: the first definition is as a "characteristic class" with values in Chow-Witt theory, while the second definition is as an "obstruction class." Along the way, we refine Morel's relative Hurewicz theorem in A^1-homotopy theory, and show how to define (twisted) Chow-Witt groups for geometric classifying spaces.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0c3a64484feefeb71d229535a97c887cc9ef8a9e
How researchers see this paper
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In Geometry and Topology
- Tom Bachmann
- K. Wickelgren
- M. Levine
- Markus Spitzweck
- O. Rondigs
- Vladimir Voevodsky
- Thomas H. Geisser
- P. Ostvaer
In Mathematical Physics
- Tom Bachmann
- K. Wickelgren
- M. Levine
- Markus Spitzweck
- O. Rondigs
- P. Ostvaer
- Marc Hoyois
- Thomas H. Geisser
Citations in the corpus
- EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS (2020, background): “Asok and Fasel show that the latter agrees with π∗e (V, ρ) up to a unit in GW(k) [AF16].”
- Aspects of Enumerative Geometry with Quadratic Forms (2017, methodology): “er class of a vector bundle V with that of its dual (Theorem 11.1): e(V) = (−h−1i)rankVe(V∨), where h−1iis the one-dimensional form q(x) = −x2. The proof of this uses the interpretation by Asok-Fasel [4] of the Euler class as an obstruction class. Kass-Wickelgren1 have constructed an Euler number in”