Show simple item record

Topological restrictions on Anosov representations

dc.contributor.authorCanary, Richard
dc.contributor.authorTsouvalas, Konstantinos
dc.date.accessioned2020-09-02T15:02:36Z
dc.date.availableWITHHELD_16_MONTHS
dc.date.available2020-09-02T15:02:36Z
dc.date.issued2020-12
dc.identifier.citationCanary, Richard; Tsouvalas, Konstantinos (2020). "Topological restrictions on Anosov representations." Journal of Topology 13(4): 1497-1520.
dc.identifier.issn1753-8416
dc.identifier.issn1753-8424
dc.identifier.urihttps://hdl.handle.net/2027.42/156496
dc.description.abstractWe characterize groups admitting Anosov representations into SL(3,R), projective Anosov representations into SL(4,R), and Borel Anosov representations into SL(4,R). More generally, we obtain bounds on the cohomological dimension of groups admitting Pk‐Anosov representations into SL(d,R) and offer several characterizations of Benoist representations.
dc.publisherTata Institute of Fundamental Research
dc.publisherWiley Periodicals, Inc.
dc.subject.other22E40 (primary)
dc.titleTopological restrictions on Anosov representations
dc.typeArticle
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbtoplevelScience
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/156496/2/topo12166_am.pdfen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/156496/1/topo12166.pdfen_US
dc.identifier.doi10.1112/topo.12166
dc.identifier.sourceJournal of Topology
dc.identifier.citedreferenceF. Kassel and R. Potrie, ‘Eigenvalue gaps for hyperbolic groups and semigroups’, Preprint, 2002, arXiv:2002.07015.
dc.identifier.citedreferenceB. Bowditch, ‘ Cut points and canonical splittings of hyperbolic groups ’, Acta Math. 180 ( 1998 ) 145 – 186.
dc.identifier.citedreferenceK. Tsouvalas, ‘ On Borel Anosov representations in even dimensions ’, Comment. Math. Helv., to appear.
dc.identifier.citedreferenceM. Kapovich, Hyperbolic manifolds and discrete groups, Progress in Mathematics 183 ( Birkhäuser, Basel, 2001 ).
dc.identifier.citedreferenceM. Kapovich, ‘ Convex projective structures on Gromov‐Thurston manifolds ’, Geom. Topol. 11 ( 2007 ) 1777 – 1830.
dc.identifier.citedreferenceI. Kapovich and N. Benakli, ‘ Boundaries of hyperbolic groups ’, Combinatorial and geometric group theory, Contemporary Mathematics 296 ( American Mathematical Society, Providence, RI, 2002 ) 39 – 93.
dc.identifier.citedreferenceM. Kapovich, B. Leeb and J. Porti, ‘ Anosov subgroups: dynamical and geometric characterizations ’, Eur. Math. J. 3 ( 2017 ) 808 – 898.
dc.identifier.citedreferenceM. Kapovich, B. Leeb and J. Porti, ‘ A Morse Lemma for quasigeodesics in symmetric spaces and Euclidean buildings ’, Geom. Topol. 22 ( 2018 ) 3827 – 3923.
dc.identifier.citedreferenceF. Kassel, ‘ Geometric structures and representations of discrete groups ’, Proceedings of the I.C.M., vol. 2 (eds B. Sirakov, P. N. de Souza and M. Viana; World Scientific, 2019 ) 1113 – 1150.
dc.identifier.citedreferenceH. Wilton, ‘ Essential surfaces in graph pairs ’, J. Amer. Math. Soc. 31 ( 2018 ) 893 – 919.
dc.identifier.citedreferenceF. Labourie, ‘ Anosov flows, surface groups and curves in projective space ’, Invent. Math. 165 ( 2006 ) 51 – 114.
dc.identifier.citedreferenceG. S. Lee and L. Marquis, ‘ Anti‐de Sitter strictly GHC‐regular groups which are not lattices ’, Trans. Amer. Math. Soc. 372 ( 2019 ) 153 – 186.
dc.identifier.citedreferenceL. Louder and N. Touikan, ‘ Strong accessibility for finitely presented group ’, Geom. Topol. 21 ( 2017 ) 1805 – 1835.
dc.identifier.citedreferenceJ. Morgan, ‘ On Thurston’s uniformization theorem for three‐dimensional manifolds ’, Pure Appl. Math. 112 ( 1984 ) 37 – 125.
dc.identifier.citedreferenceJ. Morgan and G. Tian, The geometrization conjecture ( American Mathematical Society, Providence, RI, 2014 ).
dc.identifier.citedreferenceS. J. Patterson, ‘ Lectures on measures on limit sets of Kleinian groups ’, Analytical and geometric aspects of hyperbolic space (ed. D. B. A. Epstein; Cambridge University Press, Cambridge, 1987 ) 281 – 323.
dc.identifier.citedreferenceM. Pozzetti, A. Sambarino and A. Wienhard, ‘ Conformality for a robust class of non‐conformal attractors ’, J. Reine Angew. Math., to appear.
dc.identifier.citedreferenceP. Scott, ‘ Compact submanifolds of 3‐manifolds ’, J. Lond. Math. Soc. 7 ( 1974 ) 246 – 250.
dc.identifier.citedreferenceR. Swan, ‘ Groups of cohomological dimension one ’, J. Algebra 12 ( 1969 ) 585 – 610.
dc.identifier.citedreferenceT. Zhang and A. Zimmer, ‘Regularity of limit sets of Anosov representations’, Preprint, 2019, arXiv:1903.11021.
dc.identifier.citedreferenceA. Zimmer, ‘ Projective Anosov representations, convex cocompact actions, and rigidity ’, J. Differential Geom., to appear.
dc.identifier.citedreferenceH. Abels, G. Margulis and G. Soifer, ‘ Semigroups containing proximal linear maps ’, Israel J. Math. 91 ( 1995 ) 1 – 30.
dc.identifier.citedreferenceW. Abikoff and B. Maskit, ‘ Geometric decompositions of Kleinian groups ’, Amer. J. Math. 99 ( 1977 ) 687 – 697.
dc.identifier.citedreferenceJ. F. Adams, ‘ On the non‐existence of elements of Hopf invariant one ’, Ann. of Math. 72 ( 1960 ) 20 – 104.
dc.identifier.citedreferenceJ. Baez, ‘ The octonions ’, Bull. Amer. Math. Soc. 39 ( 2002 ) 145 – 205.
dc.identifier.citedreferenceT. Barbot, ‘ Three‐dimensional Anosov flag manifolds ’, Geom. Top. 14 ( 2010 ) 153 – 191.
dc.identifier.citedreferenceY. Benoist, ‘ Propriétés asymptotiques des groupes linéaires ’, Geom. Funct. Anal. 7 ( 1997 ) 1 – 47.
dc.identifier.citedreferenceY. Benoist, ‘ Convexes divisibles II ’, Duke Math. J. 120 ( 2003 ) 97 – 120.
dc.identifier.citedreferenceY. Benoist, ‘ Convexes divisibles I ’, Algebraic groups and arithmetic, Tata Institute of Fundamental Research Studies in Mathematics 17 ( Tata Institute of Fundamental Research, Mumbai, 2004 ).
dc.identifier.citedreferenceY. Benoist, ‘ Convexes divisibles III ’, Ann. Sci. Éc. Norm. Supér (4) 38 ( 2005 ) 793 – 832.
dc.identifier.citedreferenceY. Benoist, ‘ Convexes hyperboliques et quasiisométries ’, Geom. Dedicata 122 ( 2006 ) 109 – 134.
dc.identifier.citedreferenceY. Benoist, ‘ A survey on divisible convex sets ’, Geometry, analysis and topology of discrete groups (eds S. G. Dani and G. Prasad; International Press, Vienna, 2008 ) 1 – 18.
dc.identifier.citedreferenceM. Bestvina and G. Mess, ‘ The boundary of negatively curved groups ’, J. Amer. Math. Soc. 4 ( 1991 ) 469 – 481.
dc.identifier.citedreferenceR. Bieri, ‘ Mayer‐Vietoris sequences for HNN‐groups and homological duality ’, Math. Z. 143 ( 1975 ) 123 – 130.
dc.identifier.citedreferenceJ. Bochi, R. Potrie and A. Sambarino, ‘ Anosov representations and dominated splittings ’, J. Eur. Math. Soc. 11 ( 2019 ) 3343 – 3414.
dc.identifier.citedreferenceG. E. Bredon and J. W. Wood, ‘ Non‐orientable surfaces in orientable 3‐manifolds ’, Invent. Math. 7 ( 1969 ) 83 – 110.
dc.identifier.citedreferenceR. Canary, M. Lee, A. Sambarino and M. Stover, ‘ Amalgam Anosov representations ’, Geom. Topol. 21 ( 2017 ) 215 – 251.
dc.identifier.citedreferenceK. Corlette, ‘ Archimedean superrigidity and hyperbolic geometry ’, Ann. of Math. (2) 135 ( 1992 ) 165 – 182.
dc.identifier.citedreferenceJ. Danciger, F. Guéritaud and F. Kassel, ‘ Convex cocompactness in pseudo‐Riemannian hyperbolic spaces ’, Geom. Dedicata. 192 ( 2018 ) 87 – 126.
dc.identifier.citedreferenceJ. Danciger, F. Guéritaud and F. Kassel, ‘Convex cocompact actions in real projective geometry’, Preprint, 2017, arXiv:1704.08711.
dc.identifier.citedreferenceJ. Danciger, F. Guéritaud, F. Kassel, G. S. Lee and L. Marquis, ‘Convex cocompactness for Coxeter groups’.
dc.identifier.citedreferenceJ. Danciger and T. Zhang, ‘ Affine actions with linear Hitchin part ’, Geom. Funct. Anal. 29 ( 2019 ) 1369 – 1439.
dc.identifier.citedreferenceD. Fisher and T. J. Hitchman, ‘ Strengthening Kazhdan’s property (T) by Bochner methods ’, Geom. Dedicata. 160 ( 2012 ) 333 – 364.
dc.identifier.citedreferenceM. Gromov and R. Schoen, ‘ Harmonic maps into singular spaces and p‐adic superrigidity for lattices in groups of rank one ’, Inst. Hautes Études Sci. Publ. Math. 76 ( 1992 ) 165 – 246.
dc.identifier.citedreferenceF. Guéritaud, O. Guichard, F. Kassel and A. Wienhard, ‘ Anosov representations and proper actions ’, Geom. Topol. 21 ( 2017 ) 485 – 584.
dc.identifier.citedreferenceO. Guichard, ‘ Composantes de Hitchin et représentations hyperconvexes de groupes de surface ’, J. Differential Geom. 80 ( 2008 ) 391 – 431.
dc.identifier.citedreferenceO. Guichard and A. Wienhard, ‘ Anosov representations: domains of discontinuity and applications ’, Invent. Math. 190 ( 2012 ) 357 – 438.
dc.identifier.citedreferenceN. Hitchin, ‘ Lie groups and Teichmüller space ’, Topology 31 ( 1992 ) 449 – 473.
dc.identifier.citedreferenceW. Hurewicz, ‘ Sur la dimension des produits Cartesiens ’, Ann. of Math. (2) 36 ( 1935 ) 194 – 197.
dc.identifier.citedreferenceW. Hurewicz and H. Wallman, Dimension theory ( Princeton University Press, Princeton, NJ, 1941 ).
dc.identifier.citedreferenceD. Johnson and J. Millson, ‘ Deformation spaces associated to compact hyperbolic manifolds ’, Discrete groups in geometry and analysis, Progress in Mathematics 67 (ed. R. Howe; Birkhäuser, Basel, 1987 ) 48 – 106.
dc.owningcollnameInterdisciplinary and Peer-Reviewed


Files in this item

Show simple item record

Remediation of Harmful Language

The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.

Accessibility

If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.