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Tagged with kt.k-theory-and-homology smooth-manifolds
7 questions
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Smooth version of the splitting principle
Inspried by this MO question A manifold whose tangent space is a sum of line bundles and higher rank vector bundles we pose the following question as a possible smooth version of the splitting ...
- 356
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A roof genus of high dimensional lens space
Let $p$ be a natural number, and for $i\in \{0,
..., p-1\}$,
denote the irreducible rank one complex representation of $\mathbb{Z}/p$. by $\rho_{i}$.
Let $a=(a_{1},\ldots a_{d}) $ ...
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7
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Have examples of non-simple connected higher-dimensions integer homology sphere?
We known that there exists smooth integer homology n-sphere (n>4) with some non-trivial fundamental group by the Kervaire theorem [Michel A. Kervaire, MR 253347 Smooth homology spheres and their ...
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12
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Homotopy spheres with vanishing and non-vanishing $\alpha$-invariant
I'm unsure whether this question is appropriate for mathoverflow, so feel free to criticize.
All manifolds are closed, smooth and have dimensions $n\ge 5$.
The Atiyah-Shapiro-Bott-Orientation gives ...
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1
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1
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Integration from vector bundles
Let $(E,M,p)$ be a smooth n dimensional vector bundle. Then $(TE,TM,Dp)$ is a 2n dimensional vector bundle. We restrict this bundle to $M\subset TM$. We denote this restricted bundle by $F$, as a ...
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4
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Totally non parallelizable manifold
Does there exist a manifold M which all iterated tangent bundles are non parallelizable manifolds? That is$ M, TM , T^2(M), \ldots ,T^n(M)\ldots$ are non parallelizable manifold?
What is ...
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11
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2
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The ring $C^{\infty}(M)$?
Let $M$ be a smooth paracompact manifold. I think that the ring $C^{\infty}(M)$ contains many (possibly almost all?) geometric or topological information about $M$.
(e.g. Let $E$ be a vector bundle ...
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