Questions tagged [whitehead-product]

A product on the homotopy groups of a space: $\pi_k(X)\times\pi_l(X) \to \pi_{k+l-1}(X)$.

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Sum of higher Whitehead products

For a CW-complex $X$ and homotopy classes $[f_i] \in \pi_{l_i}(X)$ for $1 \leq i \leq s$, where $s \geq 2$, the higher Whitehead product is defined to be the set $$[f_1,...,f_s] := \{[\rho \circ \phi] ...
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10 votes
1 answer

Whitehead product and a homotopy group of a wedge sum

Note : this is a crosspost from the Mathematics StackExchange, as suggested by this meta post. Let $X$ be an $n$-connected ($n\geqslant1$) CW-complex and $Y$ be a $k$-connected ($k\geqslant1$) CW-...
  • 243
7 votes
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"Relative Whitehead products"

The notion of a relative Whitehead product exists in the literature and has been asked about before (e.g. here). I am trying to find out about a different product on relative homotopy classes which ...
  • 188
5 votes
1 answer

CW Product via Whitehead map

Product CW-complexes are defined via characteristic maps rather than from attaching maps, so via maps from $\mathbb D^n$ rather than from $\mathbb S^{n-1}$, because we have the propriety that $\mathbb ...
  • 263
16 votes
1 answer

Whitehead products and Framed Manifolds

The attaching map for the top cell of the torus $S^n \times S^n$ is a map $$ [x,y]: S^{2n-1} \to S^n \vee S^n $$ where the notation is such that $x,y : S^n \to S^n \vee S^n$ are the two inclusions–––...
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Reference request: Whitehead product and the Borel construction

This is a question about signs. Fix a based space $(X,x_0)$, a topological group $G$ acting on $X$ from the left, so that the basepoint $x_0$ is fixed, a based map $\alpha\colon S^p\to G$ ($p\geq1$)...
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