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Homotopy theory, homological algebra, algebraic treatments of manifolds.

21 votes
1 answer
2k views

What are simplicial topological spaces intuitively?

(This is a repost of a question from MSE. I hope there is more to say.) I tend to imagine simplicial objects in a category as some kind of "topological objects", with a notion of homotopy. Simplicial …
Dmitry Pirozhkov's user avatar
7 votes
1 answer
688 views

Homologically distinct infinite loop structures on a space

Let $X$ be a connected pointed topological space equipped with two different actions of $E_\infty$-operad. Each action provides a collection of deloopings $X_i$, where $X_0 = X$ and $\Omega X_i$ is ho …
Dmitry Pirozhkov's user avatar