arXiv subjects
Publications and source records attributed to Lewis Tadman.
In this paper, we provide a general Sunada--Pesce--Sutton-type method that produces pairs of isospectral metric measure spaces. This construction relies on a representation theoretic assumption, and we give examples of spaces satisfying this condition, such as RCD spaces. As an application, we construct a pair of simply connected isospectral, non-isometric RCD non-Alexandrov spaces and a pair of Alexandrov non-orbifold spaces.
In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and that in fact, the intrinsic stratification agrees with the MCS stratification. As a consequence, we improve on Perelman's result and answer affirmatively a question by Fujioka.
In this paper, we give a short and self-contained proof to a 1991 conjecture by Moore concerning the structure of certain finite-dimensional Gromov--Hausdorff limits, in the ANR setting. As a consequence, one easily characterizes finite dimensional limits of PL-able or Riemannian $n$-manifolds with a uniform contractibility function. For example, one can define for any compact connected metric space that is a resolvable ANR homology manifold of covering dimension at least 5, an obstruction, which vanishes if and only if the homology manifold can be approximated in the Gromov--Hausdorff sense by PL-manifolds of the same dimension and with a uniform contractibility function. Further, it provides short proofs to certain well known results by reducing them to problems in Bing topology. We also give another proof using more classical arguments that yield more structural information. We give several applications to the theory of homology manifolds, Alexandrov spaces, Wasserstein spaces and a generalized form of the diffeomorphism stability conjecture.