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Results tagged with homotopy-theory
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user 4149
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
4
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Is a complex or real algebraic variety homotopically equivalent to a CW complex?
Let $k$ be either the field $\Bbb C$ of complex numbers or the field $\Bbb R$ of real numbers.
Let $X$ be an algebraic variety over $k$, say, quasi-projective and smooth (but not necessarily projectiv …
- 14.2k
16
votes
Non-isomorphic complex Lie groups with the same exceptional Lie algebra for $\mathfrak{g_2,f...
I prefer to use the language of algebraic groups.
All algebraic groups and Lie algebras are defined over $\Bbb C$.
1. Let ${\mathfrak g}$ be a semisimple Lie algebra.
Consider the automorphism group $ …
- 14.2k