Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorgregprice
   • CommentTimeMay 14th 2023
   • PermaLink
   Author: gregprice
   Format: MarkdownItexThis gives the idea and definition of a pseudoorientation, and the key properties related to integration. The definition is taken from [[integration of differential forms]], and the rest is largely from my reading of several of Toby's messages in the linked Usenet thread. It'd be good to add some examples, particularly with n=2 and n=3, including in the electromagnetism context where one traditionally uses a right-hand rule to conflate orientations with pseudoorientations (and 2- with 1- and pseudo- with untwisted forms). A couple of the messages in that thread had some nice examples, but I don't have the specific messages in front of me at the moment. I may return to this in the next few days to try to track those down. <a href="https://ncatlab.org/nlab/revision/pseudoorientation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/pseudoorientation">current</a>

   This gives the idea and definition of a pseudoorientation, and the key properties related to integration. The definition is taken from integration of differential forms, and the rest is largely from my reading of several of Toby’s messages in the linked Usenet thread.

   It’d be good to add some examples, particularly with n=2 and n=3, including in the electromagnetism context where one traditionally uses a right-hand rule to conflate orientations with pseudoorientations (and 2- with 1- and pseudo- with untwisted forms). A couple of the messages in that thread had some nice examples, but I don’t have the specific messages in front of me at the moment. I may return to this in the next few days to try to track those down.

   v1, current