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Results tagged with homotopy-theory
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user 61536
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
3
votes
On the homotopy type of $\mathbb{QP}^\infty$
It is nice that you asked a question about the space $\mathbb Q P^\infty$. I have thought about this space for a long time and came to the conclusion that $\mathbb Q P^\infty$ is the most "regular" sp …
- 41.8k
2
votes
Accepted
Do Locally Contractible, Path-Connected Groups have Accessible Bases?
For your restricted question the answer is affirmative. It follows from the following theorem of Yagasaki:
Theorem. For any subpolyhedron $X$ in a connected 2-manifold $M$, the connected component of …
- 41.8k
14
votes
What is the fewest number of points you must delete from $\mathbb{R}^3$ to make it not simpl...
The simply connected deletion number equals the continuum. This follows from the fact that for any dense subset $A$ in the real line the subset $A_3=(A\times \mathbb R\times \mathbb R)\cup (\mathbb R\ …
- 41.8k