arXiv subjects

Sam Nariman

Publications and source records attributed to Sam Nariman.

20 records · Page 2Linked to original sources

arXiv2017

Stable homology of surface diffeomorphism groups made discrete

We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that $C^{\infty}$-diffeomorphisms and volume preserving diffeomorphisms of surfaces as family of discrete groups exhibit homological stability. We show that the stable homology of $C^{\infty}$-diffeomorphims of surfaces as discrete groups is the same as homology of certain infinite loop space related to Haefliger's classifying space of foliations of codimension 2. We use this infinite loop space to obtain new results about (non)triviality of characteristic classes of flat surface bundles.

math.AT↗

arXiv2016

On powers of the Euler class for flat circle bundles

Apparently a lost theorem of Thurston states that the cube of the Euler class $e^3\in H^6(BDiff^δ_ω(S^1);\mathbb{Q})$ is zero where $Diff^δ_ω(S^1)$ is the analytic orientation preserving diffeomorphisms of the circle with the discrete topology. This is in contrast with Morita's theorem that the powers of the Euler class are nonzero in $H^*(BDiff^δ(S^1);\mathbb{Q})$ where $Diff^δ(S^1)$ is the orientation preserving $C^{\infty}$- diffeomorphisms of the circle with the discrete topology. The purpose of this short note is to prove that the powers of the Euler class $e^k \in H^*(BDiff^δ_ω(S^1);\mathbb{Z})$ in fact are nonzero in cohomology with integer coefficients. We also give a short proof of Morita's theorem.

math.GT↗