Ricardo Andrade

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Name Ricardo Andrade
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 comment Equivariant versus retractive spaces: a reference request
On the other hand, the above article makes a reference to "Parametrized spaces model locally constant homotopy sheaves" (arxiv.org/abs/0706.2874) by Michael Shulman. Corollary 8.7 in this article is very close to the result that John Klein is asking for.
1h
 comment Equivariant versus retractive spaces: a reference request
It seems that article deals with unbased $G$-simplicial sets.
8h
 revised fundamental class is the sum of simplices of triangulation of the manifold?
corrected text
May
18
 comment Does the signature admit a homotopy coherent refinement?
I am unfamiliar with L-theory. Nevertheless, I came across a recent article on the arxiv which seems related: "Commutativity properties of Quinn spectra" (arxiv.org/abs/1304.4759). It states in remark 1.4 that the Sullivan-Ranicki orientation from $MSTop$ to L-theory is a ring map of symmetric ring spectra, which I assume to mean a map of associative/$A_\infty$ monoids. Immediately before that remark, it is also stated that the authors are unaware of any previous result on the multiplicativity of the symmetric signature. Perhaps this article and the references therein will be helpful.
May
16
 revised Basic results with three or more hypotheses
fixed link (replaced prime by %27); edited body
May
16
 revised Waldhausen $K$-theory for $G$-spaces
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May
16
 revised Is there an equivalent of Heisenberg’s uncertainty principle in the decision sciences ?
fixed spelling
May
16
 revised 4D TQFT from a modular tensor category
corrected spelling
May
16
 awarded ● Civic Duty
May
16
 revised Basic results with three or more hypotheses
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May
16
 comment Does there exist a space X whose suspension is homotopy equivalent to [0,1] rel ends but where X is not contractible?
@Spiros: You're welcome.
May
16
 accepted Does there exist a space X whose suspension is homotopy equivalent to [0,1] rel ends but where X is not contractible?
May
16
 revised Does there exist a space X whose suspension is homotopy equivalent to [0,1] rel ends but where X is not contractible?
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May
16
 revised Does there exist a space X whose suspension is homotopy equivalent to [0,1] rel ends but where X is not contractible?
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May
16
 revised Does there exist a space X whose suspension is homotopy equivalent to [0,1] rel ends but where X is not contractible?
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May
16
 answered Does there exist a space X whose suspension is homotopy equivalent to [0,1] rel ends but where X is not contractible?
May
9
 comment higher order Noether identities
I believe this question could use some broader, more visible tags, but I do not know what they should be.
May
9
 revised higher order Noether identities
corrected spelling
May
9
 comment Algebraic topology in low regularity
@Benoît: Indeed. Somehow, I forgot about the trace... Thank you very much for the clarification.
May
9
 comment Homotopy equivalences preserving structure
@Oscar: Thank you for the clarification. I completely misunderstood the question.
May
9
 comment Algebraic topology in low regularity
It is difficult to define the values on a set of measure zero of a "function" in an arbitrary Sobolev space. For example, the boundary of the disc, or countable sets (e.g. the values of a sequence) have Lebesgue measure zero in $\mathbb{R}^n$ for $n>1$. This happens because elements of Sobolev spaces are really equivalence classes of functions identified if they differ on a set of measure zero. As such, one has to be very careful to describe what one means by their values on a set of measure zero.
May
9
 revised Homotopy equivalences preserving structure
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May
8
 revised The classifying space of a gauge group
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May
8
 comment Homotopy equivalences preserving structure
I do not know of any references for this particular fact. However, as Jeff Strom indicates, if you have "sufficient" homotopy extension properties, then the diagram formed by the intersections of the $X_i$'s (respectively, the $Y_i$'s) should be cofibrant, and thus its colimit is equivalent to its homotopy colimit. Then the homotopy invariance of homotopy colimits in the Hurewicz/Strøm model structure on topological spaces shows that the map induced on the colimits (which are hopefully $X$ and $Y$) is a homotopy equivalence. The book by Hirschhorn contains these model categorical facts.
May
8
 comment What are some examples of weak ω-categories?
@Jeremy: Thank you for the clarification.
May
8
 revised Explicit Lie May structure on cosimplicial DG Lie algebras
corrected spelling, improved presentation
May
7
 revised Lyndon-Hochschild-Serre spectral sequence and cup products
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May
7
 revised Realizability of extensions of a free oriented matroid by an independent set
rearranged presentation
May
5
 revised When does an even-dimensional manifold fiber over an odd-dimensional manifold?
fixed spelling error
May
5
 revised Realizability of extensions of a free oriented matroid by an independent set
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May
5
 revised Realizability of extensions of a free oriented matroid by an independent set
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May
5
 revised Realizability of extensions of a free oriented matroid by an independent set
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May
5
 revised Realizability of extensions of a free oriented matroid by an independent set
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May
5
 revised Realizability of extensions of a free oriented matroid by an independent set
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May
5
 asked Realizability of extensions of a free oriented matroid by an independent set
May
4
 comment Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads
@David: I do not know whether it exists. I am not very familiar with model structures on categories of algebras over operads. I have only read about model structures on categories of algebras over cofibrant operads. Unfortunately, the commutative monoid operad is not at all cofibrant. My only other idea was to try transferring the model structure on simplicial commutative monoids to the category of topological commutative monoids. However, I could not easily see whether the conditions for the existence of the transferred model structure were verified.
May
4
 comment Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads
I sincerely hope you get a good answer to your question. It happens all too often that errors are known, yet they are described nowhere. I just have a minor nitpick. Only a path connected commutative monoid in topological spaces need be weakly equivalent to a product of Eilenberg-MacLane spaces. For example, the free commutative monoid on a space $X$ is the disjoint union of the spaces $X^{\times n}/\Sigma_n$ for $n\in\mathbb{N}$. These quotients will rarely be equivalent to products of Eilenberg-MacLane spaces: e.g. $(S^1)^{\times 2}/\Sigma_2 \simeq S^1 \vee S^1$.
May
3
 comment How does Berger-Moerdijk’s relative Boardman-Vogt work?
@Gabriel: Thank you very much for this answer. Why did the authors not correct this in the article posted on the arxiv?
May
3
 revised Is this square a push-out square?
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May
2
 comment What are some examples of weak ω-categories?
@Jeremy: Thank you very much for the explanation. I just want to make sure I understand correctly what you mean by "higher identity morphism". Would that be a degenerate simplex (or globule, etc) in some multi-simplicial or globular approach? Or maybe it is a thin simplex in a complicial approach? Is that correct? Is there a better way to think about it?
May
1
 comment Does a *topological* manifold have an exhaustion by compact submanifolds with boundary?
@Misha: Thank you very much for clarifying the references. I also agree with the sentiment that the Kirby-Siebenmann book is rather impenetrable. :(
May
1
 comment Does a *topological* manifold have an exhaustion by compact submanifolds with boundary?
It seems that Quinn's theorem in "Topological transversality holds in all dimensions" allows for a proof of the result which does not directly invoke the existence of handle decompositions. First give a proper embedding $f:M\to\mathbb{R}^N$. Then use Quinn's result to deform $f$ to some embedding $f_i :M\to\mathbb{R}^n$ which is transverse to $\partial \overline{B_i(0)}$: according to Quinn, we may assume that $f$ and $f_i$ coincide outside a small neighbourhood of $\partial \overline{B_i(0)}$. Then $M$ is exhausted by the compact locally flat submanifolds $M_i=(f_i)^{-1}(\overline{B_i(0)})$.
May
1
 revised Does a *topological* manifold have an exhaustion by compact submanifolds with boundary?
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May
1
 comment Does a *topological* manifold have an exhaustion by compact submanifolds with boundary?
@Misha: That is a very informative answer. I have a question about the references. Is the result on the existence of handle decompositions for non-compact manifolds also in the book by Kirby and Siebenmann? Or does it follow from Freedman and Quinn's work?
Apr
30
 comment What are some examples of weak ω-categories?
@Jeremy Hahn: Can you describe what an invertible morphism in a (weak) $\omega$-category would look like in the first homotopy theory you consider?
Apr
30
 awarded ● Fanatic
Apr
28
 comment Quotients of classifying spaces
@unknown (google): You are welcome. It was a fun problem to work on.
Apr
28
 accepted Quotients of classifying spaces
Apr
28
 revised Quotients of classifying spaces
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Apr
28
 revised Quotients of classifying spaces
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