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作者:Müller, Lukas , Woike, Lukas
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.27-54
摘要:We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_{\infty}$-algebras with $G$-action. For this homology theory, we establish an equivariant version of excision and prove that it ex...
作者:Choi, Suyoung , Park, Hanchul
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.97-115
摘要:A real toric space is a topological space which admits a well-behaved $\mathbb{Z}_2^k$-action. Real moment-angle complexes and real toric manifolds are typical examples of real toric spaces. A real toric space is determined by the pair of a simplicial complex $K$ and a characteri...
作者:Wilson, W. Stephen
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.11-25
摘要:We compute the homology of the spaces in the Omega spectrum for $BoP$. There is no torsion in $H_{*} (\underline{BoP}_i)$ for $i \geqslant 2$, and things are only slightly more complicated for $i \lt 2$. We find the complete homotopy type of $\underline{BoP}_i$ for $i \leqslant 6...
作者:Kamiyama, Yasuhiko
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.1-10
摘要:Let $a$ be a real number satisfying $0 \lt a \lt \pi$. We denote by $M_n (a)$ the configuration space of regular spherical $n$-gons with side-lengths $a$. The purpose of this paper is to determine $\chi (M_n (a))$ for all a and odd $n$. To do so, we construct a manifold $X_n...
作者:Arone, Gregory , Lesh, Kathryn
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.77-96
摘要:We study the equivariant homotopy type of the poset ${\mathcal{L}}_{p^k}$ of orthogonal decompositions of ${\mathbb{C}}^{p^k}$. The fixed point space of the $p$-radical subgroup $\Gamma_{k}\subset U(p^k)$ acting on ${\mathcal{L}}_{p^k}$ is shown to be homeomorphic to a symplectic...
作者:Koceić Bilan, Nikola , Mirošević, Ivančica
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.55-68
摘要:A new generalized definition of homotopy is proposed, including a new class of continuous mappings that we call box-homotopies. It turns out that to be box-homotopic is an equivalence relation on $\mathit{Top}(X,Y)$ and $\mathit{HTop}(X,Y)$, and that it is well adjusted with comp...
作者:Greenlees, J.P.C.
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.69-75
摘要:The paper identifies which couniversal spaces have suspension spectra equivalent to commutative orthogonal ring $G$-spectra for a compact Lie group $G$. Equivalently these are the couniversal spaces admitting an action of an $E_{\infty}^G$-operad. We show that they are precisely ...
作者:Chen, Zhuo , Liu, Zhangju , Xiang, Maosong
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.141-165
摘要:Motivated by Kapranov’s discovery of an $\operatorname{sh}$ Lie algebra structure on the tangent complex of a Kähler manifold and Chen–Stiénon–Xu’s construction of $\operatorname{sh}$ Leibniz algebras associated with a Lie pair, we find a general method to construc...
作者:Arlin, Kevin
来源:[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.117-139
摘要:We prove a categorified Whitehead theorem showing that the $2$-functor $\mathrm{HO}$ associating a prederivator to a quasicategory reflects equivalences. The question of whether $\mathrm{HO}$is bicategorically fully faithful (that is, whether morphisms and $2$-morphisms can be un...
作者:Edward Frenkel , Davide Gaiotto
来源:[J].Communications in Number Theory and Physics(IF 1.394), 2020, Vol.14 (2)
摘要:We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to junctions of two boundary conditions in a 4d gauge theory and can be constructed from ...

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