Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 184

Homotopy theory, homological algebra, algebraic treatments of manifolds.

66 votes
1 answer
2k views

Is there an octonionic analog of the K3 surface, with implications for stable homotopy group...

The infamous K3 surface has many constructions in many fields ranging from algebraic geometry to algebraic topology. Its many properties are well known. For this question I am really interested in the …
Chris Schommer-Pries's user avatar
45 votes

Difference between represented and singular cohomology?

This is a good question because it really hits on a subtle issue. It turns out that Johannes and Ben are both correct and incorrect at the same time unless we settle some very subtle issues. Let me ex …
Chris Schommer-Pries's user avatar
35 votes
1 answer
1k views

Finding the octonionic analog of the K3 surface, via (almost) hyperkahler geometry?

The K3 manifold is an amazing object in mathematics which plays an important role in several fields ranging from the study of smooth 4-manifolds to algebraic geometry to differential geometry and beyo …
Chris Schommer-Pries's user avatar
35 votes
Accepted

Maps inducing zero on homotopy groups but are not null-homotopic

Consider ordinary singular cohomology with varying coefficients. You can look at the short exact sequence of abelian groups: $$0 \to \mathbb{Z}/2 \to \mathbb{Z}/4 \to \mathbb{Z}/2 \to 0$$ This give …
Chris Schommer-Pries's user avatar
34 votes
2 answers
5k views

Example Wanted: When Does Čech Cohomology Fail to be the same as Derived Functor Cohomology?

I want to know exactly how derived functor cohomology and Cech cohomology can fail to be the same. I started worrying about this from Dinakar Muthiah's answer to an MO question, and Brian Conrad's com …
Chris Schommer-Pries's user avatar
31 votes
3 answers
2k views

Is the counit of geometric realization a Serre fibration?

Recall that a Serre fibration between topological spaces is a map which has the homotopy lifting property (HLP) for all CW complexes (equivalently for all disks $D^k$). The Serre fibrations are the fi …
Chris Schommer-Pries's user avatar
30 votes
Accepted

"Homotopy-first" courses in algebraic topology

I was a heavily involved TA for such a graduate course in 2006 at UC Berkeley. We started with a little bit of point-set topology introducing the category of compactly generated spaces. Then we move …
29 votes
4 answers
1k views

Which stable homotopy groups are represented by parallelizable manifolds?

The Pontryagin-Thom construction allows one to identify the stable homotopy groups of spheres with bordism classes of stably normally framed manifolds. A stable framing of the stable normal bundle ind …
Chris Schommer-Pries's user avatar
28 votes
Accepted

Nilpotence of the stable Hopf map via framed cobordism

Answer Summary Let $\eta$ be the framed 1-manifold which is the Lie group framing on the circle and let $\nu$ be the Lie group framing on $S^3 = Spin(3)$. I am probably going to conflate these framed …
Chris Schommer-Pries's user avatar
26 votes
1 answer
1k views

Why are quasitopological spaces needed in sheaf theoretic approaches to the h-principle?

Recently I have been learning more about the h-principle and in particular the methods of "continuous sheaves". In many treatments of this I see people using "quasi-topological spaces" and I am trying …
Chris Schommer-Pries's user avatar
26 votes
2 answers
2k views

Loop Spaces as Generalized Smooth spaces or as Infinite dimensional Manifolds?

There are two ways to define smooth mapping spaces and I want to know how they compare. Let's take the concrete special case of free loops spaces. I think this is the most studied example so will pro …
Chris Schommer-Pries's user avatar
25 votes
4 answers
3k views

A Peculiar Model Structure on Simplicial Sets?

I'm wondering if there is a Quillen model structure on the category of simplicial sets which generalizes the usual model structure, but where every simplicial set is fibrant? I want to use this to do …
Chris Schommer-Pries's user avatar
24 votes
6 answers
2k views

Simplicial model of Hopf map?

The Hopf fibration is a famous map $S^3\to S^2$ with fiber $S^1$, which is the generator in $\pi_3(S^2)$. We can model this map in terms simplicial sets by taking the singular simplicial sets of these …
Chris Schommer-Pries's user avatar
22 votes
4 answers
2k views

Functorial Whitehead Tower?

The Whitehead tower of a (pointed) space is a tower of spaces which successively kills the bottom homotopy groups. The first two spaces can be constructed functorially (at least for suitably nice spac …
Chris Schommer-Pries's user avatar
20 votes
Accepted

Every Manifold Cobordant to a Simply Connected Manifold

Assume that $M^n$ has $\pi_1$ finitely generated (Edit: and n>3). Choose a generator. We will construct (using surgery) a cobordism to $M'$ which kills that generator, and by induction we can kill all …
Chris Schommer-Pries's user avatar

1
2 3 4 5 6
15 30 50 per page