758 reputation
310
bio website nullplug.org
location Bonn, Germany
age 33
visits member for 3 years, 7 months
seen Apr 14 at 13:13
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
@KarolSzumiƂo: 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
@KarolSzumiƂo: 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.