Questions tagged [rational-homotopy-theory]
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111 questions
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Reference for functors in Kadeishvili's C_\infty paper
In his paper Cohomology $C_\infty$-algebra and rational homotopy type, Tornike Kadeishvili describes how the rational cohomology of a simply-connected space carries the structure of a $C_\infty$-...
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What is the best way to study Rational Homotopy Theory
I studied basic algebraic topology elements:
fundamental group, higher homotopy groups, fibre bundles, homology groups, cohomology groups, obstruction theory, etc.
I want to study Rational Homotopy ...
29
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1
answer
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Software for rational homotopy theory
Does anybody know a software manipulating commutative differential graded algebras, and providing a computation of the minimal model? I tried to use the package DGAlgebras of Macaulay2, but I got ...
- 466
18
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1
answer
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Higher homotopy algebraic structure on the homology of an operad
Given a DGA $A$, then by standard techniques such as homological perturbation theory, the ring structure on the homology $H(A)$ extends to a minimal $A_\infty$-algebra structure such that $H(A)$ is ...
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3
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A non-formal space with vanishing Massey products?
Let $X$ be a polyhedron. For each $n$-dimensional face $f$ of $X$ fix a homeomorphism $\sigma_f:\triangle^n\to f$ where $\triangle^n$ is the standard $n-$simplex so that whenever $f$ is a face of $f'$ ...
- 23.5k
30
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6
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Poincare duality and the $A_\infty$ structure on cohomology
If $X$ is a topological space then the rational cohomology of $X$ carries a canonical $A_\infty$ structure (in fact $C_\infty$) with differential $m_1: H^\ast(X) \to H^{\ast+1}(X)$ vanishing and ...
- 6,229
19
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Hodge star and harmonic simplicial differential forms
Is there a notion of harmonic forms and Hodge theory for Sullivan's piecewise smooth differential forms on a simplicial set?
Let me recall some background.
Hodge Theory on a Riemannian manifold
A ...
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5
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2
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Characterizing the rationalization of spaces.
In the category of rational spaces, loop spaces split as products of Eilenberg-Mac Lane
spaces and SUSPENSIONS split as wedges of (rational) spheres. I wonder if anything of the following form is ...
- 12.5k
27
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1
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Mixed Hodge structure on the rational homotopy type
A mixed Hodge structure (mHs) on a commutative differential graded algebra (cgda) over $\mathbf{Q}$ is a mixed Hodge structure on the underlying vector space such that the product and the differential ...
- 23.5k
6
votes
1
answer
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Rational homotopy type of a complement
Let $X$ and $X'$ be smooth closed manifolds. Take closed subpolyhedra $D\subset X$ and $D'\subset X'$ (with respect to some triangulations) and let $f:X\to X'$ be a homotopy equivalence such that $f(D)...
- 23.5k
13
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Rational homotopy theory of a punctured manifold
Let $M$ be a smooth simply connected manifold and let $N$ be $M$ minus a point. Is it possible to construct an explicit Sullivan model for $N$ (i.e. a commutative differential graded algebra (cdga) ...
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