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Results tagged with homotopy-theory
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user 3901
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.
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Classifying maps into homogeneous spaces up to homotopy
The adams spectral sequence certainly does compute the desired result. But it sounds like you are looking for something to do/understand. by homogeneous spaces do you mean G/H for two lie groups? in t …
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2
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Why are spectra indexed over the natural numbers?
The reason may be slightly historical, the first examples of spectra were most easily seen to be indexed over the natural numbers: $MU$, $HR$, and $\mathbb{S}$. Now though, we know we ought to be usin …
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0
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Notes by Bousfield
I am looking for a copy of "Operations on derived functors of non-additive functors" by Bousfield. It is referenced in many papers and is supposedly from 1967.
Obviously, and electronic copy would be …
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4
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Dyer-Lashof algebra and Steenrod algebra "duality"
This is not the duality that was asked for in the question, but it does show a way in which the Steenrod algebra structure is related to the Dyer-Lashof algebra structure. The Dyer-Lashof algebra can …
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32
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3
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How should a homotopy theorist think about sheaf cohomology?
As a student of homotopy theory or algebraic topology, I have a certain outlook as to how one ought to think of a cohomology theory. There are axioms that help us with rudimentary computations, there …
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2
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answer
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Model categories and cellular maps
A question came up on MSE and it generated, for me, the following question:
When looking at the maps of CW/cell/simplicial complexes do the cellular/simplicial maps have a model theoretic interpretati …
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4
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1
answer
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Complex orientation of the Adams Summand
First lets fix a prime $p$ (I really care about $p=2$ but would be happy to know about other primes as well). When localized at a prime the spectrum $ku$ (Complex connective K-theory) splits as a wedg …
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references / general idea of kervaire invariant problem
Snaith's book is good place to look. Also, Hopkins lecture at Atiyah's birthday is awesome. It was caled the doomsday conjecture because of what would happen in the EHP sequence if these elements were …
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1
answer
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Complex orientations on homotopy
I am wondering if there is a more "geometric" formulation of complex orientations for cohomology theories than just a computation of $E^*\mathbb{C}$P$^{\infty}$ or a statement about Thom classes. It s …
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44
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4
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Integral cohomology (stable) operations
There have been a couple questions on MO, and elsewhere, that have made me curious about integral or rational cohomology operations. I feel pretty familiar with the classical Steenrod algebra and its …
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A reference for Calculus of Functors for Model Categories
I haven't read it, but maybe this could be useful: http://arxiv.org/abs/math/0601221
Calculus of Functors and Model categories by Biedermann Chorny and Roendigs
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6
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1
answer
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Serre spectral sequence with spectra
A friend recently asked me if i had heard anything about a stable Serre Spectral Sequence or one constructed with spectra, has any one else ever heard of this? is there any reason other than historica …
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15
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1
answer
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Comodule exercises desired
This Question is inspired by a Quote of Moore's
"There are two ‘evil’ influences at work here:
1. we are toilet trained with algebras not coalgebras
2. some of us are addicted to manifolds and so th …
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