Research

Publications and Pre-prints

These are also listed on the arXiv, MathSciNet and Google Scholar.

• Rokhlin Dimension and Inductive Limit actions on AF-algebras (with Sureshkumar M)
  (under review)
  https://arxiv.org/abs/2405.17380
  We show that the crossed product of an AF-algebra by a single automorphism is an AT-algebra provided the action is approximately inner and has the Rokhlin property.


• Rokhlin Dimension: Permanence Properties and Ideal Separation (with Sureshkumar M)
  (to appear in Groups, Geometry and Dynamics)
  https://arxiv.org/abs/2305.06675
  We study Rokhlin dimension for actions of amenable, residually finite groups on C*-algebras. We prove many permanence properties, and also describe ideals in the associated crossed product C*-algebra.


• K-stability of AT-algebras (with Apurva Seth)
  (Journal of Mathematical Analysis and Applications Vol. 52, Issue 2 (2023))
  https://doi.org/10.1016/j.jmaa.2022.126957
  We compute the rational nonstable K-groups of AT-algebras, and show that such an algebra is K-stable if and only if it has slow dimension growth.


• Rational K-stability of Continuous C(X)-algebras (with Apurva Seth)
  (Journal of the Australian Mathematical Society, 115 (1) (2023), p. 119-144)
  https://www.doi.org/10.1017/S144678872200009X
  We show that a continuous field of rationally K-stable C*-algebras is rationally K-stable, provided the underlying space is a compact metric space of finite covering dimension. We also give an application to certain crossed product C*-algebras.
  


• Rokhlin Dimension and Equivariant Bundles
  (Journal of Operator Theory 87 (2) (2022), p. 487-509 )
  We study the Rokhlin dimension for natural actions of compact groups on the Cuntz-Pimsner algebra associated to a vector bundle.
  


• Homotopical Stable Ranks for certain C*-algebras associated to groups (with Anshu)
  (Studia Mathematica 261 (2021), p. 307-328)
  https://doi.org/10.4064/sm200601-17-11
  We estimate the homotopical stable ranks for certain group C*-algebras and crossed product C*-algebras. Along the way, we do so for certain C(X)-algebras as well.
  


• AF-algebras and Rational Homotopy theory (with Apurva Seth)
  (New York Journal of Mathematics 26 (2020), p. 931-949)
  We compute the rational homotopy groups of the group of quasi-unitaries of an AF-algebra, from a given Bratteli diagram. We also show that an AF-algebra is K-stable if and only if it is rationally K-stable.
  


• K-stability of Continuous C(X)-algebras (with Apurva Seth)
  (Proceedings of the AMS 148 (2020), p. 3897-3909)
  https://doi.org/10.1090/proc/15035
  We show that a continuous field of K-stable C*-algebras is itself K-stable provided the underlying space is a compact metric space of finite covering dimension.
  


• Homotopical Stable Ranks for Certain C*-Algebras
  (Studia Mathematica 247 (3) (2019), p. 299-328)
  https://doi.org/10.4064/sm180222-6-5
  We study the general and connected stable ranks for C*-algebras, focussing on pullbacks and tensor products by commutative C*-algebras.
  


• Roots of Dehn twists about Multicurves (with Kashyap Rajeevsarathy)
  (Glasgow Mathematical Journal 60 (3) (2018), p. 555-583)
  https://doi.org/10.1017/S0017089517000283
  We investigate roots of multitwists in the mapping class group of a surface, and determine necessary and sufficient conditions for the existence of such roots from combinatorial data.
  


• E-theory for C[0,1]-algebras with finitely many singular points (with Marius Dadarlat)
  (Journal of K-Theory 13 (2) (2014), p. 249-274)
  https://doi.org/10.1017/is013012029jkt252
  We investigate the equivariant E-theory of certain continuous fields of C*-algebras, and show how it relates to the K-theory sheaf.