# Tag Info

### Reference for the proof that Möbius transformations extend to isometries of hyperbolic 3-space

Probably, you can find a discussion of this in Thurston's notes on hyperbolic 3-manifolds, or maybe some of the expositions by his students. However, what you are asking for is actually pretty simple: ...
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### On the origin of a fundamental theorem of additive number theory

I shared the link to this thread with several colleagues, inviting them to contribute to the discussion. Notably, I received a response from Melvyn Nathanson himself, most of which is reproduced below ...
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### Decimal expansion definition of real numbers, constructively

We have a well defined map from decimal expansions to Cauchy real numbers, so by taking the image factorisation of this map, we can always quotient out the set of decimal expansions to get a subobject ...
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### Reference for the proof that Möbius transformations extend to isometries of hyperbolic 3-space

This holds more generally in higher dimension too, and I needed similar references about this basic fact of the so-called AdS/CFT correspondence: global conformal maps of the sphere $S^n$ are in one-...

### Clausen's modified Hodge Conjecture

In June 2024, Dustin gave a four-hour lecture series in Copenhagen, primarily aimed at explaining and motivating this modified Hodge conjecture. This was part of a "Master class" on ...
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### Reference for the proof that Möbius transformations extend to isometries of hyperbolic 3-space

MR0725161 Ahlfors, Lars V. MÃ¶bius transformations in several dimensions, Minneapolis, MN, 1981.
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### Reference for homotopy groups of filtered homotopy colimits

Here's one way to get this out of the literature: By [Lurie, Higher topos theory, Prop. 5.3.3.3], for filtered $I$ we have that the colimit functor $\mathrm{Fun}(I,\mathcal{S})\to \mathcal{S}$ ...
• 9,992
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### Number of distinct higher dimensional integer partitions

For distinct part plane partitions (called strict plane partitions $\mathcal{SP}$ in the references below), MacMahon's formula  \sum_{\pi \in \mathcal{P}} q^{|\pi|} = \prod_{n \ge 1} \left( \frac{1}{...
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