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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.

5 votes
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250 views

Existence of an affine variety with homotopy type of suspension of another affine variety

Let $X$ be an affine variety. My question is does there exist another affine variety with the homotopy type of the suspension of $X$?
1 vote
1 answer
332 views

How to compute singular homologies of affine hypersurface in $A^4$ [closed]

I was trying to compute singular homology in integer coefficient of the hypersurface $t^2-1=z^{n}+x(xy-1)$ contained in $A^4$. Can anyone help me computing that? Can anyone tell me some reference wher …