I seek for some small simplicial model of Moore spaces $M(\mathbb{Z}/k\mathbb{Z},n)$. What is the simplest way to construct such? Of course we may take some cofiber of degree $k$ map between spheres, however there is no clever model for such map and therefore for the obtained cofiber.
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$\begingroup$ There is a simple model for the degree $k$ map between $S^1$, so one can get a reasonable model for higher dimensional spheres by suspending. $\endgroup$– user43326Commented Aug 1, 2017 at 16:49
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$\begingroup$ See mathoverflow.net/questions/17771 $\endgroup$– Neil StricklandCommented Aug 1, 2017 at 16:56
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$\begingroup$ What is a simple model for degree $k$ map between $S^1$? Because if we take non-fibrant model for $S^1$ then there are only two maps $S^1 \rightarrow S^1$. $\endgroup$– SamarkandCommented Aug 1, 2017 at 20:52
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$\begingroup$ SageMath (sagemath.org) has an explicit implementation of $M(\mathbb{Z}/k\mathbb{Z}, 1)$ as a simplicial complex with $2k+3$ vertices. Then as @user43326 says, you can suspend. $\endgroup$– John PalmieriCommented Aug 1, 2017 at 20:54
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$\begingroup$ Triangulate the circle as the boundary of a $3k$-gon (that is, $3k$ vertices and $3k$ 1-simplices), and map it to the boundary of a triangle, wrapping around $k$ times. $\endgroup$– John PalmieriCommented Aug 1, 2017 at 20:55
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