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SUMMARY:Benjamin Waßermann (Karlsruhe Institute of Technology)
DTSTART:20200623T143000Z
DTEND:20200623T153000Z
DTSTAMP:20260422T151710Z
UID:GoeTop/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GoeTop/6/">T
 he $L^2$-Cheeger Müller Theorem and its applications to hyperbolic lattic
 es</a>\nby Benjamin Waßermann (Karlsruhe Institute of Technology) as part
  of Göttingen topology and geometry seminar\n\n\nAbstract\nIn this talk\,
  we examine the relationship in different contexts between the analytic an
 d the topological $L^2$-torsion of odd-dimensional manifolds. \n\nLet $M$ 
 be a compact\, smooth\, odd-dimensional manifold-with-boundary satisfying 
 $\\chi(M) = 0$ and let $\\rho \\colon \\pi_1(M) \\to \\GL(V)$ be a finite-
 dimensional unimodular representation of its fundamental group. Provided t
 hat the pair $(M\,\\rho)$ is $L^2$-acyclic and a technical determinant cla
 ss condition is satisfied\, two positive real numbers $T_{An}^{(2)}(M\,\\r
 ho)\,T_{Top}^{(2)}(M\,\\rho)$\, the analytic and topological $L^2$-torsion
  of $(M\,\\rho)$\, can be defined. \n\nWhile $T_{Top}^{(2)}(M\,\\rho)$ is 
 constructed solely with the aid of any arbitrary CW-structure on $M$\, a R
 iemannian metric on $M$ as well as a metric on the flat bundle $E_\\rho \\
 downarrow M$ associated to $\\rho$ is needed to defined $T_{An}^{(2)}(M\,\
 \rho)$.\n\nThe first part of this talk is devoted to present a recent resu
 lt\, which establishes the relationship between the two quantities and fro
 m which follows that they agree in many instances. \n\nIn the second part\
 , we will consider odd-dimensional hyperbolic manifolds of finite volume (
 in particular\, not necessarily compact spaces) and representations of the
  ambient Lie group. In this instance\, another recent result is presented 
 which extends the definition of $T_{An}^{(2)}(M\,\\rho)$ and $T_{Top}^{(2)
 }(M\,\\rho)$ and shows the equality of the two quantities in this case.\n
LOCATION:https://researchseminars.org/talk/GoeTop/6/
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