LAUSR

Isometry groups and mapping class groups of spherical 3-orbifolds

Sign Up to like & get
recommendations!
1 Published in 2018 at "Mathematische Zeitschrift"

DOI: 10.1007/s00209-018-2166-2

Abstract: We study the isometry groups of compact spherical orientable 3-orbifolds $$S^3/G$$S3/G, where G is a finite subgroup of $$\mathrm {SO}(4)$$SO(4), by determining their isomorphism type. Moreover, we prove that the inclusion of $$\text{ Isom }(S^3/G)$$Isom(S3/G)… read more here.

Keywords: spherical orbifolds; isometry groups; class groups; mapping class ... See more keywords

Commuting conjugates of finite-order mapping classes

Sign Up to like & get
recommendations!
0 Published in 2019 at "Geometriae Dedicata"

DOI: 10.1007/s10711-020-00523-9

Abstract: Let $$\text {Mod}(S_g)$$ Mod ( S g ) be the mapping class group of the closed orientable surface $$S_g$$ S g of genus $$g\ge 2$$ g ≥ 2 . In this paper, we derive necessary… read more here.

Keywords: order; mod; mapping classes; finite order ... See more keywords

Automorphisms of symmetric groups are toy examples for mapping class groups

Sign Up to like & get
recommendations!
2 Published in 2021 at "Expositiones Mathematicae"

DOI: 10.1016/j.exmath.2020.06.004

Abstract: Abstract We give a new proof establishing the automorphism groups of the symmetric groups inspired by the analogous result of Ivanov for the extended mapping class group. As a key tool, we consider the actions… read more here.

Keywords: toy examples; mapping class; automorphisms symmetric; symmetric groups ... See more keywords

Big mapping class groups and rigidity of the simple circle

Sign Up to like & get
recommendations!
1 Published in 2021 at "Ergodic Theory and Dynamical Systems"

DOI: 10.1017/etds.2020.43

Abstract: Let $\unicode[STIX]{x1D6E4}$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\unicode[STIX]{x1D6E4}$ on the circle is either trivial or semiconjugate to a unique minimal action on… read more here.

Keywords: big mapping; simple circle; class groups; mapping class ... See more keywords

Fukaya categories of surfaces, spherical objects and mapping class groups

Sign Up to like & get
recommendations!
1 Published in 2021 at "Forum of Mathematics, Sigma"

DOI: 10.1017/fms.2021.21

Abstract: Abstract We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least $2$ whose Chern character represents a nonzero Hochschild homology class is quasi-isomorphic to a simple… read more here.

Keywords: class; fukaya categories; fukaya category; categories surfaces ... See more keywords

Distortion and Tits alternative in smooth mapping class groups

Sign Up to like & get
recommendations!
1 Published in 2019 at "Transactions of the American Mathematical Society"

DOI: 10.1090/tran/7476

Abstract: In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve… read more here.

Keywords: smooth mapping; tits alternative; mapping class; cantor set ... See more keywords

Mapping class group representations from Drinfeld doubles of finite groups

Sign Up to like & get
recommendations!
1 Published in 2020 at "Journal of Knot Theory and Its Ramifications"

DOI: 10.1142/s0218216520500339

Abstract: We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group [Formula: see text], focusing on surfaces without marked points or with one marked point. We… read more here.

Keywords: group; class group; formula see; see text ... See more keywords

Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic

Sign Up to like & get
recommendations!
1 Published in 2020 at "Comptes Rendus Mathematique"

DOI: 10.5802/crmath.61

Abstract: It is well known that Sullivan showed that the mapping class group of a simply connected highdimensional manifold is commensurable with an arithmetic group, but the meaning of “commensurable” in this statement seems to be… read more here.

Keywords: arithmetic group; group; simply connected; mapping class ... See more keywords