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Mark Grant
Mark Grant
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This is in response to the OP's recent reference request.

It sounds like the reference you seek may be John Milnor's paper

Construction of universal bundles. I. Ann. of Math. (2) 63 (1956), 272–284.

Milnor constructs a universal bundle whose fibre is the space of "simplicial loops", by analogystarts with Serre's loop spacethe Serre path-loop fibration with fibre $\Omega X$ on a based countable simplicial complex $X$. He then replaces continuous paths (loops) with "simplicial paths (loops)". It turns out that thisthe resulting bundle is still universal (meaning the space of based simplicial paths is contractible) and the fibre $\tilde{\Omega} X$, the space of based simplicial loops, is now a topological group.

This is in response to the OP's recent reference request.

It sounds like the reference you seek may be John Milnor's paper

Construction of universal bundles. I. Ann. of Math. (2) 63 (1956), 272–284.

Milnor constructs a universal bundle whose fibre is the space of "simplicial loops", by analogy with Serre's loop space fibration. It turns out that this fibre is now a group.

This is in response to the OP's recent reference request.

It sounds like the reference you seek may be John Milnor's paper

Construction of universal bundles. I. Ann. of Math. (2) 63 (1956), 272–284.

Milnor starts with the Serre path-loop fibration with fibre $\Omega X$ on a based countable simplicial complex $X$. He then replaces continuous paths (loops) with "simplicial paths (loops)". It turns out that the resulting bundle is still universal (meaning the space of based simplicial paths is contractible) and the fibre $\tilde{\Omega} X$, the space of based simplicial loops, is a topological group.

Source Link
Mark Grant
Mark Grant
  • 35.9k
  • 8
  • 95
  • 198

This is in response to the OP's recent reference request.

It sounds like the reference you seek may be John Milnor's paper

Construction of universal bundles. I. Ann. of Math. (2) 63 (1956), 272–284.

Milnor constructs a universal bundle whose fibre is the space of "simplicial loops", by analogy with Serre's loop space fibration. It turns out that this fibre is now a group.