Tagged Questions

1
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0answers
34 views

Characterizing a certain subset of isotropic vectors

Dear all, I stumbled on this question due to an application in physics, but I find it hard to find useful references for it. I looked into literature on projective geometry and po …
1
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0answers
43 views

Reference request: construction of Steenrod operations for an odd p

Where in literature can one find a construction of Steenrod reduced powers (for an odd $p$) that (1) works for the singular cohomology of arbitrary topological spaces (or, more …
5
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1answer
153 views

What is an interpretation of the relation in the cohomology of the pure braid groups?

In 1968, Arnol'd proved that the integral cohomology of the pure braid group $P_n$ is isomorphic to the exterior algebra generated by the collection of degree-one classes $\omega_{ …
3
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0answers
74 views

What is the ring structure of the complex topological K-theory of a non-singular complex quadric?

I would like to know the ring structure of $K(Q_n)$ explicitly where $Q_n \subset \mathbb{P}^{n+1}$ is the non-singular $n$-dimensional complex quadric and $K(Q_n) = K^0(Q_n)$ is …
4
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0answers
52 views

In cell-decomposed manifolds, how easy is it to arrange for the tubular neighborhood of a diagonal to contract onto the diagonal?

Suppose that you have decomposed a manifold $M$ into cells (I care most, if it matters, about compact oriented smooth manifolds; but if my question can be solved in the PL category …
1
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1answer
80 views

Directed colimits of maps in a combinatorial model category

I have the following situation. $M$ is a combinatorial model category, or if you like a locally presentable $(\infty,1)$-category. I have a set of maps $S$ and I let $C$ be the cla …
5
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2answers
160 views

Is the site of (smooth) manifolds hypercomplete?

By site of manifolds Man, I mean the category of manifolds (maybe submanifolds to obtain a small category) with continuous maps between them. A Grothendieck topology is given by op …
2
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1answer
348 views

What is the 31th homotopy group of the 2 - sphere ?

What is $\pi_{31}(S^2)$, the 31th homotopy group of the 2 - sphere ? This question has a physics motivation: 1) There are relations between (2nd and 3rd) Hopf fibrations and (2 …
6
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0answers
83 views

Does the signature admit a homotopy coherent refinement?

Cobordism genera can often be refined to $E_\infty$-orientations in the sense of Ando-Blumberg-Gepner-Hopkins-Rezk: 1) the mod 2 Euler characteristic $MO\to H\mathbb{F}_2$; 2) th …
2
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0answers
59 views

Is a retract of a group of type F_n again of this type?

It has been asked here, whether a retract of a finitely presented group is again finitely presented, i.e. if $G$ is a finitely presented group and $H$ is a group which fits into a …
0
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0answers
80 views

State of the game : cohomology of principal bundles

I would like to know what has been done in terms of specific calculations for the cohomology of principal bundle. For instance, it is known (see e.g. Greub, Halperin and Vanstone's …
7
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1answer
207 views

Waldhausen $K$-theory for $G$-spaces

I would guess that the following is true, and that somebody has worked it out, but I don't recall ever seeing it. Can anyone point me to any literature on it? Let $G$ be a finite …
1
vote
1answer
143 views

Generalization of the Lefschetz fixed point theorem

I have encountered a certain generalization of the Lefschetz fixed point theorem as folklore, and I am hoping that someone out there knows its provenance or can otherwise refer me …
5
votes
1answer
161 views

Does there exist a space X whose suspension is homotopy equivalent to [0,1] rel ends but where X is not contractible?

As pointed out by David White in http://mathoverflow.net/questions/73687/when-mapping-cone-is-contractible there exists an acyclic CW-complex $X$ which is not contractible but who …
6
votes
1answer
224 views

Anomalies in the definition of Turaev’s TQFT

In his book Quantum invariants of knots and 3-manifolds page 124, Turaev defined a TQFT $\tau$ axiomatically. For a cobordism $(M, \partial_{-}M, \partial_{+}M)$, a TQFT assignes …

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