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Chapter 24 Notation
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\(I\)
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\(I^n\text{,}\) \(\partial I^n\)
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Unit
\(n\)-cube and its boundary
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\(I^{n-1}\text{,}\) \(J^{n-1}\)
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Distinguished face of
\(I^n\) and the closure of its complement in
\(\partial I^n\) (
Definition 6.1)
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\(D^n\text{,}\) \(S^n\)
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Closed unit
\(n\)-disc and
\(n\)-sphere
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\(\mathbb{C}\)
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Complex numbers;
\(\mathbb{H}\) the quaternions
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\(\mathbb{R}P^n\)
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Real projective
\(n\)-space
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\(\mathbb{C}P^n\)
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Complex projective
\(n\)-space
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\(f * g\)
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\(\pi_n(X, x_0)\)
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\(n\)-th homotopy group of
\(X\) at
\(x_0\)
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\(\pi_n(X, A, x_0)\)
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\(n\)-th relative homotopy group of the pair
\((X,A)\)
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\(\pi_q^{s}\)
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\(\operatorname{Deck}(p)\)
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\(\Sigma X\text{,}\) \(\Omega X\)
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\(\wedge\text{,}\) \(\vee\)
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\(M_f\text{,}\) \(CX\)
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\([X, Y]\text{,}\) \([X, Y]_*\)
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Free and based homotopy classes of maps
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\(K(G,n)\)
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\(X_n\)
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\(X_{\leq n}\text{,}\) \(X_{>n}\)
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\(\mathrm{Vect}_k(X)\text{,}\) \(K(X)\)
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\(BU(k)\text{,}\) \(BU\)
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\(E^r_{p,q}\text{,}\) \(E_r^{p,q}\)
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Homological and cohomological spectral sequence pages
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\(\Lambda(\ldots)\text{,}\) \(\Gamma[\,y\,]\)
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\(\simeq\)
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Homotopy equivalence;
\(\simeq_p\) for path homotopy
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\(\cong\)
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