# Questions tagged [homotopy-theory]

Two functions are homotopic, if one of them can by continuously deformed to another. This gives rise to an equivalence relation. A group called a homotopy group can be obtained from the equivalence classes. The simplest homotopy group is the fundamental group. Homotopy groups are important invariants in algebraic topology.

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### how to install the Bvph_2.0 package in mathematica.

actually, I'm not that much familiar with and I am struggling to install the Bvph_2.0 package in mathematica software to solve a problem by HAM. can anyone please guide me.
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### Proving Brouwer's fixed point theorem using fundamental groups

I am writing my bachelor thesis on the fundamental group $\pi_1(X)$ and homotopy theory. Now I was wondering if it is possible to prove Brouwer's fixed point Theorem in arbitrary dimensions using only ...
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### Are CW complexes closed under homotopy colimits?

Consider the category of topological spaces homotopy equivalent (in the strong sense) to CW complexes. Is this category closed under arbitrary homotopy colimits? how about filtered homotopy colimits? ...
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### Group/H-space structures for standard models of classifying spaces?

Let $G$ be a commutative topological group. May in his textbook, A concise course in algebraic topology, gives a model of the classifying space $BG$ so that it is a commutative topological group ...
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### Inverses in the spherical interpetration of higher homotopy groups

I have just started studying the higher homotopy groups $\pi_n(X, x_0)$ in more detail than I have before and I am getting confused about the inverse operation which makes $\pi_n(X, x_0)$ a group. I'...
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### When is a subset is homotopy type of a regular covering?

Let $X$ and $Y$ are finite CW complexes such that $X\subsetneq Y$ such that $X$ is not homotopy equivalent to $Y$. Can $X$ be homotopy type of a finite regular covering of $Y$? If Yes can we have an ...
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As written in the title, I have some trouble in showing that a specific map is anodyne. The map in question is the inclusion of $J$ inn $\Delta^n \times \Delta^1 \times \Delta^1$, where $J$ is the ...