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Associativity of a spectrum with relation to complex bordism spectrum

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#algebraic-topology #higher-category-theory #higher-homotopy-groups
96
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Categorical meaning of the two definitions of $\pi_n(X)$

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#algebraic-topology #category-theory #higher-homotopy-groups
1.7k
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Do Homotopy Groups commute with generalized filtered colimits?

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
290
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On the homology of $K(G,n)$

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#algebraic-topology #homotopy-theory #eilenberg-maclane-spaces #higher-homotopy-groups
110
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An orientable 4-manifold with completely nontrivial 2-type

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#differential-topology #homotopy-theory #fundamental-groups #4-manifolds #higher-homotopy-groups
86
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Is there any precise sense in saying that before Serre the homotopy groups of sphere could in principle have contained an infinite amount of data?

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#homotopy-theory #abelian-groups #information-theory #higher-homotopy-groups
7.1k
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Homotopy groups U(N) and SU(N): $\pi_m(U(N))=\pi_m(SU(N))$

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#algebraic-topology #lie-groups #homotopy-theory #higher-homotopy-groups
7.4k
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Homotopy groups O(N) and SO(N): $\pi_m(O(N))$ v.s. $\pi_m(SO(N))$

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#algebraic-topology #lie-groups #homotopy-theory #higher-homotopy-groups
38
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Higher homotopy groups equality question.

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#proof-explanation #higher-homotopy-groups
472
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Do trivial homotopy groups imply existence of boundary preserving homotopies?

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#algebraic-topology #differential-topology #homotopy-theory #manifolds-with-boundary #higher-homotopy-groups
101
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Another multiplication in homotopy groups of simplicial loop space

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#simplicial-stuff #higher-homotopy-groups
1.4k
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Confusion about free homotopy, based homotopy and homotopy groups

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#homotopy-theory #fundamental-groups #higher-homotopy-groups
99
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If $A\subset X$ is a deformation retract, then do we have $\pi_k(X,A)=0$?

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#algebraic-topology #homology-cohomology #homotopy-theory #higher-homotopy-groups
172
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Hatcher's proof of the Freudenthal suspension theorem, definition of the suspension map

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
157
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element of a homotopy group

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#algebraic-topology #homotopy-theory #higher-homotopy-groups

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