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Proving a function isn't homotopic to a map to the boundary

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#algebraic-topology #homology-cohomology #homotopy-theory #fixed-point-theorems
189
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How can we assume the first homology group of the complement is zero when constructing a Casson handle?

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#differential-topology #homotopy-theory #geometric-topology #fundamental-groups #4-manifolds
4.3k
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Compositions of homotopic maps are homotopic

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#algebraic-topology #homotopy-theory
32
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Isomorphism of Homotopy groups across a filtration

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#homotopy-theory #cw-complexes
345
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Which theorem of homotopy theory states that if two objects have different genus then they are not homotopy equivalent?

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#homotopy-theory
177
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Proving weak homotopy equivalence of a map

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#algebraic-topology #homotopy-theory
242
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How do I see if the induced homomorphism from the inclusion map $S^{1'}\to S^1\times S^3$ is injective

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#algebraic-topology #homotopy-theory #fiber-bundles
114
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Let $\gamma_1, \gamma_2 : I \to M$ two homotopic curves, $M$ a $C^{\infty}$ manifold. If $\omega$ is a closed $1-$form then:

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#algebraic-topology #differential-topology #homotopy-theory
328
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How to prove that the Lefschetz number is invariante under homotopy?

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#algebraic-geometry #differential-topology #homotopy-theory #intersection-theory
4.5k
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How to construct a homotopy equivalence between a mobius band and a circle?

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#algebraic-topology #homotopy-theory
166
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tom Diecks's proof of $H_1(X)\cong \pi_1(X,x_0)^{ab}$

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#algebraic-topology #homology-cohomology #homotopy-theory
922
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Hopf fibration and exact sequence in homotopy

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#reference-request #algebraic-topology #homotopy-theory #exact-sequence #hopf-fibration
116
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Can't see why particular homotopy is continuous

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#homotopy-theory #proof-explanation #fundamental-groups
1.9k
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A deformation retract that is not a strong deformation retract

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#algebraic-topology #homotopy-theory
475
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geometric realization of a simplicial complex

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#algebraic-topology #homotopy-theory #geometric-topology #simplicial-stuff #simplicial-complex

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