Questions tagged [at.algebraic-topology]
Homotopy theory, homological algebra, algebraic treatments of manifolds.
8 questions from the last 7 days
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Interpretations of the tangent Chern numbers of the complex projective spaces $CP^n$?
I've identified the generating functions for the tangent Chern numbers of the complex projective spaces $CP^n$ given in "Algebraic topology of the Lagrange inversion" by Victor Buchstaber ...
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Does a continuous variation through compact $n$ dim manifolds preserve topology?
I begin by writing the definition below that tries to capture what a continuous family /path of manifolds is. The underlying motivation behind the definition is that the transition maps should be ...
- 1,441
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Triangulated manifolds with local orientation reversal
For a (smoothly) triangulated $n$ manifold $M$, I'll say that the triangulation is amphichiral if it admits an orientation-reversing automorphism. I'll say that the triangulation is locally ...
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chain level intersection product
Let $F$ be a field and $M$ an oriented smooth $n$-manifold.
Is it always possible to construct a differential graded $F$-vector space $(C_M,d)$ equipped with a strictly coassociative coproduct $\Delta ...
- 2,165
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cellular and handle chain complex of universal covering
Let $M$ be a compact connected smooth manifold with fundamental group $\pi:=\pi_1(M)$ and universal covering $\widetilde{M}$. We can equip $M$ with a handle decomposition and we obtain the handle ...
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Goodwillie Filtration of Factorization Homology and Hochschild Homology
The factorization homology of a framed manifold $M$ with coefficient in an $E_n$-algebra $A$, $\int_M A$, is developed by Ayala and Francis. It was shown that for $M=S^1$, $\int_M A$ is the Hochschild ...
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Functoriality in exodromy
Say we have a nice topological space $X$ with two nice (finite, conical...) stratifications $A$ and $B$ such that $B$ is coarser than $A$. Then we have a natural embedding of categories of ...
- 1,247
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Orientation local system of a vector bundle
Let $p:E\to X$ be a rank $k$ real vector bundle on a paracompact space. This question is about possible definitions of the orientation local system of $E$, which should be a local system of integer ...
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