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Abstract We determine the mod $$p$$ cohomological invariants for several affine group schemes $$G$$ in characteristic $$p$$. These are invariants of $$G$$-torsors with values in étale motivic cohomology, or equivalently in Kato’s version of Galois cohomology based on differential forms. In particular, we find the mod 2 cohomological invariants for the symmetric groups and the orthogonal groups in characteristic 2, which Serre computed in characteristic not 2. We also determine all operations on the mod $$p$$ étale motivic cohomology of fields, extending Vial’s computation of the operations on the mod $$p$$ Milnor K-theory of fields.
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On volume-preserving vector fields and finite-type invariants of knots
We consider the general non-vanishing, divergence-free vector fields defined on a domain in $$3$$ -space and tangent to its boundary. Based on the theory of finite-type invariants, we define a family of invariants for such fields, in the style of Arnold’s asymptotic linking number. Our approach is based on the configuration space integrals due to Bott and Taubes.
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- Award ID(s):
- 1043009
- PAR ID:
- 10021332
- Date Published:
- Journal Name:
- Ergodic Theory and Dynamical Systems
- Volume:
- 36
- Issue:
- 03
- ISSN:
- 0143-3857
- Page Range / eLocation ID:
- 832 to 859
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/etds.2014.83
