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Results tagged with homotopy-theory
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user 4648
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
votes
Accepted
Homotopy fiber of a map between classifying spaces
One source for some of this is section 8 of May's "Classifying spaces and fibrations"
He has G and H interchanged, unfortunately uses a coset notation for what turns out to be the homotopy fibre, and …
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8
votes
Stable homotopy groups of $RP^{\infty}$
The middle column of table IV on page 82 of George W. Whitehead's "Recent Advances in homotopy theory" Regional Conference series in mathematics Number 5
lists the groups in dimensions up to 30 (inclu …
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23
votes
Accepted
Is the 4-line of the E_2 term of the classical Adams spectral sequence known?
The 4-line is determined by Wen-Hsiung Lin in "$Ext_A^{4,*}({\bf Z}/2,{\bf Z}/2) $ and $Ext_A^{5,*}({\bf Z}/2,{\bf Z}/2) $", Topology and its Applications (2008) vol 155 no.5 pp 459-496.
He gives a …
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7
votes
How do you relate the number of independent vector fields on spheres and Bott Periodicity fo...
This is not really different from Charles's answer, but you might want to look at two papers by Beno Eckmann. They construct Hurwitz-Radon matrices, and point out that this is effectively saying that …
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