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Can the rank of the homology group of an abstract simplicial complex be computed in polynomial time?

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#computer-science #computational-complexity #homotopy-theory
234
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Is there a fibration whose base, total and fibre is a Moore space?

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#homotopy-theory
1.8k
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The action of the group of deck transformation on the higher homotopy groups

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#algebraic-topology #homotopy-theory #covering-spaces
406
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graphs and homotopy extension property

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#algebraic-topology #homotopy-theory
18.5k
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An intuitive idea about fundamental group of $\mathbb{RP}^2$

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#algebraic-topology #intuition #homotopy-theory #fundamental-groups
373
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Lemma of Whitehead

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#analysis #algebraic-topology #definition #homotopy-theory
691
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What is $\pi_{31}(S^2)$?

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#homotopy-theory #hopf-fibration
802
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Is the winding number of a map $\Omega: \; S^n \mapsto S^n$ dependent on the radius of both spheres?

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#algebraic-topology #homotopy-theory #winding-number
305
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algebraic or homotopical proof for Kakutani fixed point theorem

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#algebraic-topology #game-theory #homotopy-theory #fixed-point-theorems #set-valued-analysis
132
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Removing the star without changing homology

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#algebraic-topology #homotopy-theory #homology-cohomology
162
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Is a simplicial subcomplex of a contractible simplicial CW-complex also contractible?

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#homotopy-theory #simplicial-stuff
1.3k
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Question about null-homotopic function

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#algebraic-topology #homotopy-theory
2.9k
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(weak) homotopy equivalence

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#algebraic-topology #homotopy-theory #homology-cohomology #stable-homotopy-theory
1.2k
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Spheres in different dimension are not homotopy equivalent

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#algebraic-topology #homotopy-theory
357
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For a transitive action of a path-connected group, does every path lift?

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#general-topology #homotopy-theory #topological-groups

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