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Results tagged with examples
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user 2039
For questions requesting examples of a certain structure or phenomenon
20
votes
Examples of algorithms requiring deep mathematics to prove correctness
How about the following problem:
Given an integer $n$, how many ways are there to write it as the sum of $k$ squares? Or, equivalently, in $\mathbb{R}^k$, how many lattice points (in the standard int …
6
votes
Example s.t. the unbased loop-space is not $\Omega X \times X$
Often, as in these examples, you already see the difference in rational cohomology, which can usually be computed more easily using rational homotopy theory; a Sullivan minimal model of $X$ gives a minimal …
- 12.1k
40
votes
‘Naturally occurring’ $K(\pi, n)$ spaces, for $n \geq 2$
$\DeclareMathOperator\B{B}\newcommand\TOP{\mathrm{TOP}}\newcommand\PL{\mathrm{PL}}\newcommand\BTOP{{\B}\TOP}\newcommand\BPL{{\B}\PL}$Let $\BTOP$ and $\BPL$ be the classifying spaces of topological/PL- …
- 12.1k