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Since one direction is clear (the map to BG is homotopically trivial on the handle that one adds to (C')), one has to show that two coverings are stably equivalent if their invariant is the same.
That this sort of organization can come together to find one face in a crowd and track it through multiple jurisdictions is ludicrous on a human level but trivial on a technical one.
We consider the action of G on (V times X), which is trivial on the factor V, and the given one on X.
10, that these cohomology groups stabilize with g; indeed, stabilization furnishes an inclusion of a space which is homotopically equivalent to ( mathfrak {M}_g ) inside (mathfrak {M}_{g+1} ) (alternatively, one may say that ( Map_g rightarrow Map_{g+1}), by letting the operation be trivial on the added handle).
Of course, this is all trivial on the face of it - as meaningful as coincidental birthdays - but, aside from challenging obituarists, coincidental deaths can also raise awkward questions.
Of course the Tonys were going to feel trivial on the same day that news broke of the worst mass shooting in American history.
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It is absurd that lives are snuffed out because of someone's indulgence in trivial on-the-road conversations.
Second, I don't find my friends important enough to view the trivial goings-on of their lives.
We lament the media's focus on trivial entertainment stories on the one hand, and on bad news stories on the other.
They demonstrate that convergence is non-trivial on complex branching structures.
We also find a projective representation of the full identity component of the affine automorphism group of the Hilbert Schmidt version of the tube domain with trivial cocycle on the subgroup corresponding to the trace class version, but non-trivial on the large group.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com