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作者:Lorenzo Guerra
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.957-982MSP
摘要:We describe a Hopf ring structureon $ \bigoplus_{n \geq 0} H^* ( \Sigma_n; \mathbb{Z}_p ) $,discovered by Stricklandand Turner,where $ \Sigma_n $ is the symmetric group of $ n $ objects and $ p $ is anodd prime.We also describe an additive basis on which the cup product isexplici...
作者:John Holler , Igor Kriz
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.741-763MSP
摘要:We compute the complete $\mathop{\operatorname{RO}}(G)$--graded coefficients of ``ordinary'' cohomologywith coefficients in $\Z/2$ for $G=(\Z/2)^n$. As an important intermediatestep, we identify the ring of coefficients of the corresponding geometricfixed point spectrum, revealin...
作者:Nicholas Kuhn , Luís Pereira
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.1105-1130MSP
摘要:If $\mathcal{O}$ is a reduced operad in a symmetric monoidal category of spectra($S$--modules),an $\mathcal{O}$--algebra $I$ can be viewed as analogous tothe augmentation ideal of an augmented algebra. From the literatureon topological Andr\'e--Quillen homology, one cansee that s...
作者:Karol Szumiło
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.765-791MSP
摘要:We prove that the homotopy theory of cocomplete quasicategories isequivalent to the homotopy theory of cofibration categories. This isachieved by presenting both theories as fibration categories andconstructing an explicit exact equivalence between them.
作者:Hoang Kim Nguyen
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.1021-1040MSP
摘要:We show an equivalence of infinite loop spaces between the classifying spaceof the cobordism category with infinite loop space structure induced bytaking disjointunion of manifolds and the infinite loop space associatedto the Madsen--Tillmann spectrum.
作者:Theo Johnson-Freyd
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.917-956MSP
摘要:A topological quantum field theory is \emph{hermitian} if it is bothoriented andcomplex-valued, and orientation-reversal agrees withcomplex conjugation. A field theory \emph{satisfies spin-statistics} ifit is both spin and super, and $360^\circ$--rotation of the spin structureagr...
作者:Prasit Bhattacharya , Philip Egger , Mark Mahowald
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.657-692MSP
摘要:\advance \leftskip by -3pt\advance \rightskip by -3ptThe spectrum $Y:= M_2(1) \wedge C\eta $ admits eight $v_1$-self-maps ofperiodicity $1$. These eight self-maps admit four different cofibers,which we denote by $A_1[ij]$ for $i,j\in\{0,1\}$. We show that each ofthese four spectr...
作者:Jonathan Beardsley
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.1151-1162MSP
摘要:\advance\leftskip-1pt\advance\rightskip-1ptWe show that a large number of Thom spectra,that is, colimits ofmorphisms $BG\to\nobreak B\operatorname{GL}_1(\mathbb{S})$, can be obtained as iterated Thomspectra, that is, colimits of morphisms $BG\to B\operatorname{GL}_1(M\mkern-4mu f...
作者:Alejandro Adem , José Gómez , John Lind ...
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.869-893MSP
摘要:Using a constructionderived from the descending central series of the free groups,we produce filtrations by infinite loop spaces of the classicalinfinite loop spaces $B\operatorname{SU}$, $\mathit{BU}$, $B\operatorname{SO}$,$\mathit{BO}$,$B\operatorname{Sp}$, $B\operatorname{GL}_...
作者:Andrew Lobb , Patrick Orson , Dirk Schütz
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.1261-1281MSP
摘要:We extend Lipshitz and Sarkar's definition of a stable homotopy type associatedto a link $L$ whose cohomology recovers the Khovanov cohomology of $L$.Given an assignment $c$ (called a \emph{coloring}) of positive integer toeach component of a link $L$, we define a stable homotopy...

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