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On mod p Ap–spaces
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...
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    The mapping cone formula in Heegaard Floerhomology and Dehn surgery on knots in S3
    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...
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      Eigenvalue varieties of Brunnian links
      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...
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        Spectral sequences in smooth generalized cohomology
        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 ...
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          Translation surfaces and the curve graph in genus two
          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$\what{\mathcal{C}\mkern3mu}\mkern-3mu_{\operatorname{cyl}}$ ...
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            A refinement of Betti numbers and homology in the presence of a continuous function, I
            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...
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              Acylindrical group actions on quasi-trees
              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...
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                Non-L–space integral homology 3–spheres withno nice orderings
                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.
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                  Homotopy decompositions of gauge groups over real surfaces
                  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...
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                    The C2–spectrum Tmf1(3) and its invertiblemodules
                    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-...
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