bio | website | nullplug.org |
---|---|---|
location | Bonn, Germany | |
age | 33 | |
visits | member for | 3 years, 7 months |
seen | Apr 14 at 13:13 | |
stats | profile views | 432 |
I am a postdoc at the University of Bonn and the Max-Planck Institute for Mathematics. My interests broadly revolve around computations in homotopy theory.
Oct 31 |
comment |
Formal n-buds from BU(n) rather than SU(n)
The $\Omega SU(n)$ filtration is a filtration by loop maps. Their Thom spectra inherit a product from the loop structure which you use to make their homotopy groups into a ring. You do not have this structure for $BU(n)$. |
Oct 25 |
comment |
The Image of the Mod 2 Homology of BSp in the Homology of BSO
I am not sure that it has exactly what you are looking for, but Neil Strickland's thesis contains an astounding amount of information about the homology of K-theoretic spaces, such as those in your question. Even if it does not answer your question, it might help you with many related questions. |
Oct 1 |
comment |
Loops and suspensions of higher categories
Exactly, or one could check that the appropriate comma category is weakly contractible. |
Sep 27 |
awarded | Self-Learner |
Sep 27 |
revised |
Loops and suspensions of higher categories
Added credit. |
Sep 25 |
accepted | Loops and suspensions of higher categories |
Sep 25 |
revised |
Loops and suspensions of higher categories
Added credit and fixed a comma |
Sep 25 |
answered | Loops and suspensions of higher categories |
Sep 5 |
comment |
Loops and suspensions of higher categories
@KarolSzumiĆo: The reason I glued two copies of $E[1]$ together is that I wanted a homotopy pushout that I could map out of to construct the homotopy pullback modeling $\Omega\mathcal{C}$. I need both a $(\infty,n)$ category that corepresents $Aut(1)$ and a presentation of that a category as a homotopy pushout which corepresents $\Omega$. |
Sep 5 |
comment |
Loops and suspensions of higher categories
@KarolSzumiĆo: So one way to take what you said and get your characterization of $\Omega\mathcal{C}$ is to say that if we glue two copies of $E[1]$ together along the discrete subcategory with two objects (and do this as pointed $(\infty,n)$-categories) we get a category which corepresents the loop functor. I guess this category is supposed to be equivalent to the free $(\infty,n)$ category (in some sense) on the category with one object and one non-trivial automorphism? This intuitively makes sense. Do you have a model where this is easy to show? |
Sep 5 |
comment |
Loops and suspensions of higher categories
Karol, thanks for the clarification. I would guess that this would make the suspension similar to how I defined it, but we would also need to make all the objects in the free monoidal category invertible under the monoidal product before realizing it as a higher category. |
Sep 5 |
comment |
Loops and suspensions of higher categories
Do you have a proof that $\Omega\mathcal{C}$ is the automorphisms? In particular, why is it always an $(\infty,0)$-category? |
Sep 5 |
comment |
Loops and suspensions of higher categories
By homotopy pullback/pushout, I will take any construction that is equivalent to the derived pullback/pushout constructed using the projective/injective model structures on diagrams in a combinatorial model category modelling $(\infty,n)$-categories. |
Sep 5 |
asked | Loops and suspensions of higher categories |
Aug 27 |
awarded | Yearling |
Jul 14 |
answered | Where should I search for resolutions? |
Jul 2 |
awarded | Scholar |
Jul 2 |
comment |
Correspondence between operads and $\infty$-operads with one object
If I understand this right, you can take the multicolored operad coming out of your equivalence and take a sub singly colored operad which is weakly equivalent to it. This would give the desired simplicial operad. |
Jul 2 |
accepted | Correspondence between operads and $\infty$-operads with one object |
Jul 1 |
revised |
Correspondence between operads and $\infty$-operads with one object
Further clarification of what I mean by up to equivalence. |