scholarly journals Homotopy theory of homotopy algebras

2020 ◽  
Vol 70 (2) ◽  
pp. 683-738
Author(s):  
Bruno Vallette
Keyword(s):  
Homotopy Theory ◽  
Homotopy Algebras

Cyclicity in homotopy algebras and rational homotopy theory

2018 ◽  
Vol 25 (4) ◽  
pp. 545-570
Author(s):  
Hiroshige Kajiura
Keyword(s):  
Homotopy Theory ◽  
Decomposition Theorem ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Homotopy Algebras

AbstractKadeishvili proposes a minimal{C_{\infty}}-algebra as a rational homotopy model of a space. We discuss a cyclic version of this Kadeishvili{C_{\infty}}-model and apply it to classifying rational Poincaré duality spaces. We classify 1-connected minimal cyclic{C_{\infty}}-algebras whose cohomology algebras are those of{(S^{p}\times S^{p+2q-1})\sharp(S^{q}\times S^{2p+q-1})}, where{2\leq p\leq q}. We also include a proof of the decomposition theorem for cyclic{A_{\infty}}and{C_{\infty}}-algebras.

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

scholarly journals Double Copy from Homotopy Algebras

2021 ◽  
Vol 69 (8-9) ◽  
pp. 2100075 ◽  
Author(s):  
Leron Borsten ◽  
Hyungrok Kim ◽  
Branislav Jurčo ◽  
Tommaso Macrelli ◽  
Christian Saemann ◽  
...  
Keyword(s):  
Homotopy Algebras ◽  
Double Copy

scholarly journals A First Approximation to Homotopy Theory

1953 ◽  
Vol 39 (7) ◽  
pp. 655-660 ◽  
Author(s):  
E. H. Spanier ◽  
J. H. C. Whitehead
Keyword(s):  
Homotopy Theory ◽  
First Approximation
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