作者：Ruizhi Huang , Jie Wu 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2125-2144MSP 摘要：We prove a necessary condition for the existence ofan $A_p$--structure on$\operatorname{mod}\ p$spaces, and also derive a simple proof for the finitenessof the number of $\operatorname{mod}\ p$ $A_p$--spaces of given rank. As a directapplication, we compute a list of possible typ...
 作者：Fyodor Gainullin 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.1917-1951MSP 摘要：We write down an explicit formula for the $+$ version of the HeegaardFloer homology(as an absolutely graded vector space over an arbitraryfield) of the results of Dehn surgery on a knot $K$ in $S^3$ in terms ofhomological data derived from $\operatorname{CFK}^\infty(K)$.This allo...
 作者：François Malabre 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2039-2050MSP 摘要：In this article, it is proved that the eigenvalue variety of theexterior of a nontrivial, non-Hopf, Brunnian link in $\mathbb{S}^{3}$contains a nontrivial component of maximal dimension.Eigenvalue varieties were first introduced to generalize the$A$--polynomial of knots in $\math...  作者：Daniel Grady , Hisham Sati 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2357-2412MSP 摘要：We consider spectral sequences in smooth generalized cohomologytheories, includingdifferential generalized cohomology theories. The main differentialspectral sequences will beof the Atiyah--Hirzebruch (AHSS) type, where we provide a filtrationby the {\v C}ech resolutionof smooth ...  作者：Duc-Manh Nguyen 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2177-2237MSP 摘要：\vspace*{-7pt}\lineskiplimit-1ptLet$S$be a (topological) compact closed surface of genus two. We associate toeach translation surface$(X,\omega) \in\Omega\mathcal{M}_2=\mathcal{H}(2)\sqcup\mathcal{H}(1,1)$a subgraph$\what{\mathcal{C}\mkern3mu}\mkern-3mu_{\operatorname{cyl}}$...  作者：Dan Burghelea 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2051-2080MSP 摘要：We propose a refinement of the Betti numbers and the homology withcoefficients in a field of a compact ANR$X$, in the presence of a continuousreal-valued function on~$X$.The refinement of Betti numbers consists of finite configurations of pointswith multiplicities in the complex...  作者：Sahana Balasubramanya 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2145-2176MSP 摘要：A group$G$is acylindrically hyperbolic if it admits a non-elementaryacylindrical actionon a hyperbolic space. We prove that everyacylindrically hyperbolic group$G$has a generating set$X$suchthat the corresponding Cayley graph$\Gamma$is a (non-elementary)quasi-tree and the...  作者：Xinghua Gao 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2511-2522MSP 摘要：\lineskip-1ptWe give infinitely many examples of non-L--space irreducibleinteger homology$3$--spheres whose fundamental groups do not have nontrivial$\widetilde{\operatorname{PSL}}_2(\mathbb{R})$representations.  作者：Michael West 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2429-2480MSP 摘要：We analyse the homotopy types of gauge groups of principal$U(n)$--bundles associated to pseudoreal vector bundles in thesense of Atiyah.We providesatisfactoryhomotopydecompositions of these gauge groups intofactors in which the homotopy groups are well known. Therefore,we substan...  作者：Michael Hill , Lennart Meier 来源：[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.1953-2011MSP 摘要：We explorethe$C_2$--equivariant spectra$\operatorname{Tmf}_1(3)$and$\operatorname{TMF}_1(3)$. In particular,we compute their$C_2$--equivariant Picard groups and the$C_2$--equivariantAnderson dual of$\operatorname{Tmf}_1(3)\$. This implies corresponding results for thefixed-...