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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-...

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