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作者:Ulrich Bunke
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1285-1385MSP
摘要:We discussa universal bordism invariant obtained from theAtiyah--Patodi--Singer $\eta$--invariant from the analytic andhomotopy-theoretic point of view.Classical invariants like the Adams $e$--invariant, $\rho$--invariantsand $\operatorname{String}$--bordism invariants are derive...
作者:Jason Behrstock , Mark Hagen , Alessandro Sisto
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1731-1804MSP
摘要:In the context of $\operatorname{CAT}(0)$ cubical groups,we develop an analogue of the theory of curve complexes and subsurfaceprojections. The role of the subsurfaces isplayed by a collection of convex subcomplexes called a \emph{factorsystem}, and the role of the curve graph is...
作者:François Béguin , Christian Bonatti , Bin Yu
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1837-1930MSP
摘要:We provewe can build (transitive or nontransitive)Anosov flows on closed three-dimensional manifolds by gluingtogether filtrating neighborhoods of hyperbolic sets. We give severalapplications of this result; for example:\begin{enumerate}\item We build a closed three-dimensional m...
作者:Larsen Louder , Nicholas Touikan
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1805-1835MSP
摘要:A hierarchy of a group is a rooted tree of groups obtained byiteratively passing to vertex groups of graphs of groupsdecompositions. We define a (relative) slender JSJ hierarchy for(almost) finitely presented groups and show that it is finite,provided the group in question doesn'...
作者:Jeffrey Meier , Alexander Zupan
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1583-1630MSP
摘要:We show that the only closed $4$--manifolds admitting genus-twotrisections are\mbox{$S^2 \times S^2$} and connected sums of $S^1 \times S^3$,${\mathbb{CP}}^2$ and $\smash{\overline{\mathbb{CP}}}^2$with two summands. Moreover,each of these manifolds admits a unique genus-two trise...
作者:Federico Cantero , Oscar Randal-Williams
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1387-1467MSP
摘要:We study the space of oriented genus-$g$ subsurfaces of a fixedmanifold $M$ and, in particular, its homological properties. Weconstruct a ``scanning map'' which compares this space to the space ofsections of a certain fibre bundle over $M$ associated to its tangentbundle, and sho...
作者:Rune Haugseng
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1631-1730MSP
摘要:We introduce simple models for associative algebras and bimodules inthe context of nonsymmetric $\infty$--operads, and use these to construct an$(\infty,2)$--category of associative algebras, bimodules andbimodule homomorphisms in a monoidal $\infty$--category. By working with{$\...
作者:John Etnyre , David Vela-Vick , Rumen Zarev
来源:[J].Geometry & Topology(IF 0.974), 2017, Vol.21 (3), pp.1469-1582MSP
摘要:\vspace{-8pt}Using contact-geometric techniques and sutured Floer homology,we present an alternate formulation of the minus and plusversions of knot Floer homology. We further show how naturalconstructions in the realm of contact geometry give rise tomuch of the formal structure ...
作者:Stefan Buschenhenke , Detlef Müller , Ana Vargas
来源:[J].Analysis & PDE, 2017, Vol.10 (4), pp.817-891MSP
摘要:The problem of $L^q(\mathbb{R}^3)\to L^2(S)$ Fourier restriction estimates forsmooth hypersurfaces $S$ of finite type in $\mathbb{R}^3$ is by now very wellunderstood for a large class of hypersurfaces, including all analyticones. In this article, we take up the study of more gene...
作者:Giulio Romani
来源:[J].Analysis & PDE, 2017, Vol.10 (4), pp.943-982MSP
摘要:We study the ground states of the following generalization of theKirchhoff--Love functional,\[J_\sigma(u)=\int_\Omega\frac{(\Delta u)^2}{2} -(1-\sigma)\!\int_\Omega \det(\nabla^2u)-\int_\Omega F(x,u),\]where $\Omega$ is a bounded convex domain in $\mathbb{R}^2$ with $C^{1,1}$boun...

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