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A motivic Grothendieck–Teichmüllergroup
作者：Ismaël Soudères
来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.635-685MSP
摘要：We prove the Beilinson--Soul\'e vanishingconjecture formotives attached to the moduli spaces $\mathcal{M}_{0,n}$ of curves of genus$0$ with$n$ marked points. As part of the proof, we also show that thesemotives aremixed Tate. As a consequence of Levine's work, we thus obtain awel...
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    A combinatorial description of topological complexity for finite spaces
    作者：Kohei Tanaka
    来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.779-796MSP
    摘要：This paper presents a discrete analog of topological complexityfor finite spaces using purely combinatorial terms. We demonstratethat this coincides with the genuine topological complexity ofthe original finite space. Furthermore, we study therelationship withsimplicial complexit...
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      Euler characteristics and actions of automorphism groups of free groups
      作者：Shengkui Ye
      来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1195-1204MSP
      摘要：Let $M^{r}$ be a connected orientable manifold with the Eulercharacteristic$\chi(M)\not \equiv 0\operatorname{mod}6$. Denote by$\operatorname{SAut}(F_{n})$the unique subgroup of index two in the automorphism group of a freegroup.Then any group action of $\operatorname{SAut}(F_{n}...
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        Incomplete Tambara functors
        作者：Andrew Blumberg , Michael Hill
        来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.723-766MSP
        摘要：For a ``genuine'' equivariant commutative ring spectrum $R$,$\pi_0(R)$ admits a rich algebraic structure known as a Tambarafunctor. This algebraic structure mirrors the structure on $R$arising from the existence of multiplicative norm maps. Motivated bythe surprising fact that Bo...
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          Correction to the article Preorientations of the derived motivic multiplicative group
          作者：Jens Hornbostel
          来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1257-1258MSP
          摘要：We correct a claim concerningmotivic $S^1$--deloopings.
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            Γ–structures and symmetric spaces
            作者：Bernhard Hanke , Peter Quast
            来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.877-895MSP
            摘要：$\Gamma\mkern-1.5mu$--structures are weak forms of multiplications on closedoriented manifolds. As wasshown by Hopf the rational cohomologyalgebras ofmanifolds admitting $\Gamma\mkern-1.5mu$--structures are free over odd-degreegenerators.We prove that this condition is also suffi...
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              A rank inequality for the annular Khovanovhomology of 2–periodic links
              作者：Melissa Zhang
              来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1147-1194MSP
              摘要：For a $2\!$--periodic link $\tilde L$ in the thickened annulus and itsquotient link $L$, we exhibit a spectral sequence with\[E^1 \cong \operatorname{AKh}(\tilde L) \otimes_{\mathbb{F}} \mathbb{F}[\theta, \theta^{-1}]\rightrightarrows E^\infty \cong \operatorname{AKh}(L)\otimes_{...
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                The spectrum for commutative complexK–theory
                作者：Simon Gritschacher
                来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1205-1249MSP
                摘要：We study commutative complex $K$--theory, a generalised cohomologytheory built from spaces of ordered commuting tuples in the unitarygroups. We show that the spectrum for commutative complex $K$--theory isstably equivalent to the $k\mkern-1.5mu u$--group ring of $B\mkern-2mu U(1)...
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                  Quasi-invariant measures for some amenable groups acting on the line
                  作者：Nancy Guelman , Cristóbal Rivas
                  来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1067-1076MSP
                  摘要：Weshow that if $G$ is a solvable group acting on the lineand if there is $T\in G$ having no fixed points, then there is a Radonmeasure $\mu$ on the line quasi-invariant under~$G\!$. In fact, our methodallows for the same conclusion for $G$ inside a class of groups that isclosed u...
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                    Relative 2–Segal spaces
                    作者：Matthew Young
                    来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.975-1039MSP
                    摘要：We introduce a relative version of the $2\mskip-1.5mu$--Segal simplicial spacesdefined by Dyckerhoff and Kapranov, and G\'{a}lvez-Carrillo, Kock andTonks. Examples of relative $2\mskip-1.5mu$--Segal spaces include the categorifiedunoriented cyclic nerve, real pseudoholomorphic po...
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