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Contractability of topological space

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#algebraic-topology #differential-topology #homotopy-theory
375
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What is the third homotopy group of $SO(5)$?

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#algebraic-topology #differential-topology #homotopy-theory
131
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Must one space be the loop space of other

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
625
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How to determine the map between the singular homology groups of a torus induced by a linear map $f:\mathbb R^2 \to \mathbb R^2$?

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#algebraic-topology #homology-cohomology
311
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why the boundary of loop is zero?

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#algebraic-topology #homology-cohomology #simplicial-complex
346
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Homology and embedded surfaces of genus $g$

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#algebraic-topology #homology-cohomology #geometric-topology
2.1k
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Example for not deformation retraction but retraction

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#algebraic-topology
66
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Ways to see the connected sum of $h$ copies of $\mathbb{RP}^2$ minus a point

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#algebraic-topology
214
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Prove that $S^2 \times S^2$ is obtained by attaching a 4-cell to $S^2 ∨ S^2$

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#algebraic-topology
47
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Replacing $H$-space multiplication with a fibration

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#algebraic-topology #homotopy-theory #monoid #fibration
907
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Using fundamental polygons to prove $PR^2\# T^2 = PR^2\# PR^2 \# PR^2$.

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#algebraic-topology #surfaces #non-orientable-surfaces
643
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Why Euler characteristic is additive on a short exact sequence?

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#differential-geometry #algebraic-geometry #algebraic-topology
188
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degeneracy of the Serre spectral sequence

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#algebraic-topology #homology-cohomology #spectral-sequences #fibration
515
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Let $q : S^{2n+1} → CP^n$ be the usual quotient map. Is $q$ a covering space?

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#algebraic-topology
366
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Showing that the diagonal of $X\times X$ is transversal to the graph of $f$. (1.5.10 Guillemin and Pollack)

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#differential-geometry #algebraic-topology #differential-topology #geometric-topology #transversality

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