Charles Rezk
|
Registered User
|
I'm a homotopy theorist at the University of Illinois, with interests ranging from higher category theory to p-divisible groups.
|
|
May 16 |
awarded | ● Favorite Question |
|
May 8 |
comment |
Homotopy classes of maps Just a note: that journal is hard to find, but if your library subscribes to Elsevier you may have access to it, but under a different name. See plus.google.com/115215145654669548294/posts/… |
|
May 2 |
awarded | ● Enlightened |
|
May 2 |
awarded | ● Nice Answer |
|
Apr 9 |
comment |
Commutativity of Tor To relate this to the usual definition of Tor (derived functors of $M\otimes -$ or $-\otimes N$), presumably you need to show that the derived tensor product $M\otimes^L N$ can be computed by resolving only one of the two factors. Doesn't that require some kind of double-complex type argument? |
|
Apr 8 |
awarded | ● Popular Question |
|
Mar 26 |
awarded | ● Enlightened |
|
Mar 26 |
awarded | ● Nice Answer |
|
Mar 19 |
answered | On the naturality of the bar construction |
|
Mar 12 |
awarded | ● Notable Question |
|
Mar 8 |
comment |
Nearby homomorphisms from compact Lie groups are conjugate I'm worried about averaging $h(x)=h(x)^y*h(y)$ over $x$. In the local coordinates, $x\mapsto x^y$ isn't linear, and a non-linear transformation might not play well with the integral. |
|
Mar 8 |
awarded | ● Nice Question |
|
Mar 7 |
comment |
Nearby homomorphisms from compact Lie groups are conjugate This is very helpful! Though I'm a little confused by the penultimate paragraph, since it seems that by this point we've shown that $Z^1=B^1$. Looking at Weil's paper, it seems that the deformation theory already tells us that $\mathrm{Hom}(K,G)$ is a manifold (assuming $K$ finitely generated), and so we are done once we have $H^1=0$. |
|
Mar 6 |
answered | When is the projective model structure cartesian? When is the internal hom invariant? |
|
Mar 5 |
comment |
Nearby homomorphisms from compact Lie groups are conjugate Claudio: it goes in a nice direction, but I don't see that it gets there. The claim is true for $\mathrm{Hom}(U(1),U(1))$, but false for $\mathrm{Hom}(\mathbb{R}, U(1))$, so I don't see how I can prove it purely from Lie algebra considerations. As Misha suggests, I probably need to know something about $H^1(K,\mathfrak{g})$, not just $H^1(\mathfrak{k},\mathfrak{g})$. What I'm missing is probably really easy. |
|
Mar 5 |
asked | Nearby homomorphisms from compact Lie groups are conjugate |
|
Feb 22 |
awarded | ● Enlightened |
|
Feb 22 |
awarded | ● Nice Answer |
|
Feb 20 |
comment |
How to see the quaternionic hopf map generates the stable 3-stem? The first thing to comes to mind is derive it from $\pi_3 MSpin=0$. Is there a geometric proof that 3-dimensional spin manifolds bound? |
|
Feb 19 |
comment |
Where is there a treatment of “exponential monads”? Martin: that would probably be this, if the two monoidal structures otimes and + are actually the same. I'm interested in a case where they are not. |
|
Feb 18 |
accepted | Is it possible to obtain the vectors orthogonal to a given one by orthogonal transformations? |
|
Feb 17 |
awarded | ● Nice Question |
|
Feb 17 |
revised |
Is it possible to obtain the vectors orthogonal to a given one by orthogonal transformations? Added explicit formula for R-H number.; added 47 characters in body |
|
Feb 17 |
answered | Is it possible to obtain the vectors orthogonal to a given one by orthogonal transformations? |
|
Feb 16 |
awarded | ● Good Answer |
|
Feb 9 |
awarded | ● Nice Answer |
|
Feb 6 |
awarded | ● Popular Question |
|
Jan 24 |
awarded | ● Popular Question |
|
Jan 24 |
answered | Discovering and selecting conferences |
|
Jan 10 |
comment |
What is a simplicial commutative ring from the point of view of homotopy theory? One clue to think about: if k has finite characteristic, then simplicial commutative rings come with a natural Frobenius endomorphism. E-infinity rings don't generally have anything like that. |
|
Dec 23 |
comment |
Internal categories in simplicial sets I'm not aware that anyone has done this. I thought about this idea at one time, but dropped it when I realized that putting a suitable model category structure on simplicial objects in simplicial sets gave everything I wanted (i.e., a cartesian model category). Someone should do this. |
|
Dec 22 |
comment |
What is geometrically the Pontryagin class? A related question (which I don't know the answer to): What was Pontryagin's motivation for introducing theses classes? (And if it wasn't him, who did introduce them, why?) |
