Two kinds of orientability/orientation for a differentiable manifold
Another notion of orientability is the existence of an atlas whose transition functions have derivatives with everywhere positive determinant. This gives a clear cut way, along with the …
Orientability of spacetime - Physics Stack Exchange
Time-orientability is a mix between topology and geometry: a manifold is time orientable if there exists "an arrow of time" on it. Mathematically this means that there must be a non-vanishing …
general relativity - Is time orientability independent of space ...
Sep 17, 2021 · To see that time- and space-orientability together would imply overall orientability, just note that timelike and spacelike vector fields are necessarily linearly independent of each …
Non-orientability in electromagnetism - Physics Stack Exchange
May 10, 2024 · Where the non-orientability of the space would come into play is in which vector fields and charge configurations would be admissible in such a space. This would not strictly …
at.algebraic topology - Meaning of orientation/orientability over …
So while ℤ/m-coefficients may not be the most interesting coefficient systems to study orientability in, they're part of a larger systematic family of questions (and they don't take much extra work …
(Time-)Orientability in the Language of Fiber Bundles
Mar 19, 2024 · In general relativity books, such as Wald's, orientability and time-orientability are defined differently. As far as I remember, a spacetime is orientable if one can choose a …
gr.group theory - Is orientability a miracle? - MathOverflow
Mar 14, 2022 · Or is the existence of orientability itself a miraculous fact? EDIT: Let me make a few additional comments to nudge the discussion in a more technical and less opinion-based …
Orientability of a Complex Manifold - Physics Stack Exchange
Mar 28, 2018 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Orientability of $6$-manifold and vanishing of every Euler class
Dec 24, 2024 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Causal structure, time orientability and equivalence classes
Judging from the linked wikipedia article I suppose the purpose of this question is to understand the notion of time orientability. My answer will focus on the geometric picture behind it. I will …