作者：Müller, Lukas , Woike, Lukas 来源：[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.27-54波士顿国际出版社 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波士顿国际出版社 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波士顿国际出版社 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 $i \leqslant 6...  作者：Kamiyama, Yasuhiko 来源：[J].Homology, Homotopy and Applications, 2020, Vol.22 (1), pp.1-10波士顿国际出版社 摘要：Let$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波士顿国际出版社 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波士顿国际出版社 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波士顿国际出版社 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波士顿国际出版社 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波士顿国际出版社 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：Richard Hain 来源：[J].Pure and Applied Mathematics Quarterly(IF 0.718), 2020, Vol.16 (2) 摘要：In this paper, we give an exposition of the elliptic KZB connection over the universal elliptic curve and use it to compute the limit mixed Hodge structure on the unipotent fundamental group of the first order Tate curve. We also give an explicit algebraic formula for the restric...