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Different definitions of (co)homology with local coefficients

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#algebraic-topology #homology-cohomology #homotopy-theory
278
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Serre fibrations have HLP against all CW complexes

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#algebraic-topology #homotopy-theory #cw-complexes #fibration
32
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complex integration paths

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#complex-analysis #complex-numbers #homology-cohomology #homotopy-theory #complex-integration
104
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When does a cofibration induce a cofibration on cylinder objects?

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#category-theory #homotopy-theory #model-categories
578
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On the mapping cylinder inclusion $i : X \hookrightarrow M_f$ being a cofibration.

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#general-topology #algebraic-topology #category-theory #homotopy-theory #cofibrations
60
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Commutativity of monoid object on $\mathcal{D}$-spaces

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#algebraic-topology #category-theory #homotopy-theory #monoidal-categories #stable-homotopy-theory
983
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Commuting elements in product fundamental group

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#general-topology #algebraic-topology #homotopy-theory
153
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Equivalence between the Dwyer-Kan loop groupoid and the fundamental groupoid

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#algebraic-topology #homotopy-theory #simplicial-stuff #groupoids
128
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group homomorphism $\Phi: \pi_1(X,x_0)^{ab}\to H_1(X,\mathbb{Z})$ where $\pi_1(X,x_0)^{ab}$ is the abelianization of the group $\pi_1(X,x_0)$.

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#abstract-algebra #general-topology #algebraic-topology #homological-algebra #homotopy-theory
86
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Is $\mathbb{CP}^4 \vee S^5$ homotopy equivalent to any compact manifold without boundary?

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#algebraic-topology #smooth-manifolds #homotopy-theory
709
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Is $S^1$ a retract of the torus $T$?

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#general-topology #homotopy-theory
85
Views

Confusion about Hurewicz isomorphism

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#homology-cohomology #homotopy-theory #eilenberg-maclane-spaces
78
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Does an $X$ exist so $X \simeq \Omega^n Y$ for all $n$, and X is not an infinite loop space?

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#algebraic-topology #homotopy-theory #stable-homotopy-theory
162
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About an exact homotopy sequence

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#algebraic-topology #homotopy-theory
160
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How do synthetic homotopy groups relate to the usual homotopy groups?

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

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