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04310aam a2200601 i 4500 001 0F8A8A7C177D11EC850ADFAD22ECA4DB 003 SILO 005 20210917010313 008 210501t20212021riua b 000 0 eng 010 $a 2021016979 020 $a 1470444224 020 $a 9781470444228 035 $a (OCoLC)1228931492 040 $a LBSOR/DLC $b eng $e rda $c DLC $d OCLCO $d OCLCF $d MNU $d OCLCO $d NUI $d SILO 042 $a pcc 100 1 $a Albin, Pierre, $d 1976- $e author. 245 10 $a Resolvent, heat kernel, and torsion under degeneration to fibered cusps / $c Pierre Albin, FreÌdeÌric Rochon, David Sher. 264 1 $a Providence, Rhode Island : $b American Mathematical Society, $c [2021] 300 $a v, 126 pages : $b illustrations ; $c 26 cm. 490 1 $a Memoirs of the American Mathematical Society, $x 0065-9266 ; $v number 1314 500 $a "January 2021, volume 269, number 1314 (fifth of 7 numbers)." 504 $a Includes bibliographical references (pages 123-126). 505 0 $a Fibered cusp surgery metrics -- Pseudodifferential operator calculi -- Resolvent construction -- Projection onto the eigenspace of small eigenvalues -- Surgery heat space -- Solving the heat equation -- The R-torsion on manifolds with boundary -- The intersection R-torsion of Dar and L2-cohomology -- Analytic torsion conventions -- Asymptotics of analytic torsion -- A Cheeger-Muller theorem for fibered cusp manifolds. 520 $a "Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary"--Provided by publisher. 650 0 $a Riemannian manifolds. 650 0 $a Symmetric spaces. 650 0 $a Torsion theory (Algebra) 650 0 $a Resolvents (Mathematics) 650 0 $a Heat equation. 650 0 $a Kernel functions. 650 0 $a Surfaces, Algebraic $x Degenerations. 650 0 $a Surgery (Topology) 650 7 $a Heat equation. $2 fast $0 (OCoLC)fst00953865 650 7 $a Kernel functions. $2 fast $0 (OCoLC)fst00986892 650 7 $a Resolvents (Mathematics) $2 fast $0 (OCoLC)fst01095609 650 7 $a Riemannian manifolds. $2 fast $0 (OCoLC)fst01097804 650 7 $a Surfaces, Algebraic $x Degenerations. $2 fast $0 (OCoLC)fst01139298 650 7 $a Surgery (Topology) $2 fast $0 (OCoLC)fst01139395 650 7 $a Symmetric spaces. $2 fast $0 (OCoLC)fst01140808 650 7 $a Torsion theory (Algebra) $2 fast $0 (OCoLC)fst01152871 650 7 $a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Elliptic equations on manifolds, general theory. $2 msc 650 7 $a Global analysis, analysis on manifolds-- Partial differential equations on manifolds; differential operators -- Heat and other parabolic equation methods for PDEs on manifolds. $2 msc 650 7 $a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Spectral problems; spectral geometry; scattering theory on manifolds. $2 msc 650 7 $a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Determinants and determinant bundles, analytic torsion. $2 msc 650 7 $a Algebraic topology -- Homology and cohomology theories -- Homology with local coefficients, equivariant cohomology. $2 msc 650 7 $a Algebraic topology -- Homology and cohomology theories -- Intersection homology and cohomology in algebraic topology. $2 msc 700 1 $a Rochon, FreÌdeÌric, $d 1978- $e author. 700 1 $a Sher, David $q (David A.), $d 1987- $e author. 773 18 $w 990007620060202771 $g no:31858071391704 830 0 $a Memoirs of the American Mathematical Society ; $v no. 1314, $x 0065-9266 941 $a 1 952 $l OVUX522 $d 20220317023247.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=0F8A8A7C177D11EC850ADFAD22ECA4DBInitiate Another SILO Locator Search