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pro vyhledávání: '"Linowitz, Benjamin"'
Autor:
Linowitz, Benjamin
In a recent paper Garoufalidis and Reid constructed pairs of 1-cusped hyperbolic 3-manifolds which are isospectral but not isometric. In this paper we extend this work to the multi-cusped setting by constructing isospectral but not isometric hyperbol
Externí odkaz:
http://arxiv.org/abs/2307.09718
Autor:
Lauret, Emilio A., Linowitz, Benjamin
Publikováno v:
New York J. Math. 30 (2024), 682-721
The spectral geometry of negatively curved manifolds has received more attention than its positive curvature counterpart. In this paper we will survey a variety of spectral geometry results that are known to hold in the context of hyperbolic manifold
Externí odkaz:
http://arxiv.org/abs/2305.10950
Autor:
Heck, Laurel, Linowitz, Benjamin
In this paper we study the systoles of arithmetic hyperbolic 2- and 3-manifolds. Our first result is the construction of infinitely many arithmetic hyperbolic 2- and 3-manifolds which are pairwise noncommensurable, all have the same systole, and whos
Externí odkaz:
http://arxiv.org/abs/2204.06530
The systole of a closed Riemannian manifold is the minimal length of a non-contractible closed loop. We give a uniform lower bound for the systole for large classes of simple arithmetic locally symmetric orbifolds. We establish new bounds for the tra
Externí odkaz:
http://arxiv.org/abs/2102.01673
Autor:
Linowitz, Benjamin
Two number fields are said to be Brauer equivalent if there is an isomorphism between their Brauer groups that commutes with restriction. In this paper we prove a variety of number theoretic results about Brauer equivalent number fields (e.g., they m
Externí odkaz:
http://arxiv.org/abs/1804.07367
In this paper we study the systole growth of arithmetic locally symmetric spaces up congruence covers and show that this growth is at least logarithmic in volume. This generalizes previous work of Buser and Sarnak as well as Katz, Schaps and Vishne w
Externí odkaz:
http://arxiv.org/abs/1710.00071
The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is a fundamental invariant of the topology of M via Mostow-Prasad Rigidity. Motivated by this, the second author and Reid defined a two-dimensional analogue of the geo
Externí odkaz:
http://arxiv.org/abs/1707.03079
Publikováno v:
C. R. Math. Acad. Sci. Paris 355 (2017), 1121-1126
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessarily commensurable. While this is known to be true for arithmetic hyperbolic 3-manifolds, the non-arithmetic case is still open. Building towards a ne
Externí odkaz:
http://arxiv.org/abs/1705.08034
Autor:
Linowitz, Benjamin
It is a longstanding problem to determine the precise relationship between the geodesic length spectrum of a hyperbolic manifold and its commensurability class. A well known result of Reid, for instance, shows that the geodesic length spectrum of an
Externí odkaz:
http://arxiv.org/abs/1702.08062
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