Hairy graph construction yields nontrivial rational homotopy classes proving infinite-dimensionality of π_•(Emb_c(R^{n-2}, R^n)) ⊗ Q for odd n ≥ 5.
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For cocommutative Hopf dialgebras the set-like rack is naturally isomorphic to the conjugation rack of the group-like digroup, and every finite generalized digroup arises as the group-like elements of its digroup algebra.
For a local vector bundle V over M, the bundle S^⊠(S^⊗(V)) is the free commutative 2-algebra generated by V, and skew-symmetric maps V ⊠ V to the unit induce compatible Poisson brackets on the resulting equivariant 2-algebra bundle over configuration spaces.
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
Every free symmetric connected multiplicative operad carries a differential graded Hopf algebra structure, extending the Malvenuto-Reutenauer result.
citing papers explorer
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Infinite-dimensionality of the rational homotopy groups of the space of long embeddings of codimension 2
Hairy graph construction yields nontrivial rational homotopy classes proving infinite-dimensionality of π_•(Emb_c(R^{n-2}, R^n)) ⊗ Q for odd n ≥ 5.
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Cocommutative Hopf Dialgebras and Rack Combinatorics
For cocommutative Hopf dialgebras the set-like rack is naturally isomorphic to the conjugation rack of the group-like digroup, and every finite generalized digroup arises as the group-like elements of its digroup algebra.
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Equivariant Poisson 2-Algebra Bundles over Configuration Spaces
For a local vector bundle V over M, the bundle S^⊠(S^⊗(V)) is the free commutative 2-algebra generated by V, and skew-symmetric maps V ⊠ V to the unit induce compatible Poisson brackets on the resulting equivariant 2-algebra bundle over configuration spaces.
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On formality of diagrams of Eilenberg-MacLane spaces
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
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Differential graded Hopf algebra structure on free symmetric cosimplicial operads
Every free symmetric connected multiplicative operad carries a differential graded Hopf algebra structure, extending the Malvenuto-Reutenauer result.
- The quantum group structure of long-range integrable deformations