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010 a| 2021016979;

020 a| 9781470444228q| (paperback);

020 z| 9781470464660q| (pdf);

035 a| (WaSeSS)ssj0002477716;

040 a| LBSOR/DLCb| engc| DLCd| WaSeSS;

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050 00 a| QA649b| .A393 2021;

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084 a| 58J05a| 58J35a| 58J50a| 58J52a| 55N25a| 55N332| msc;

100 1 a| Albin, Pierre,d| 1976-?| UNAUTHORIZED;

245 10 a| Resolvent, heat kernel, and torsion under degeneration to fibered cuspsh| [electronic resource] /c| Pierre Albin, Frédéric Rochon, David Sher.;

260 a| Providence, Rhode Island :b| American Mathematical Society,c| [2021];

263 a| 2107;

300 a| pages cm.;

490 0 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.;

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.;

506 a| Available only to authorized users.;

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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Riemannian manifolds.=| ^A39401;

650 0 a| Symmetric spaces.=| ^A39159;

650 0 a| Torsion theory (Algebra)=| ^A36923;

650 0 a| Resolvents (Mathematics)=| ^A576716;

650 0 a| Heat equation.=| ^A68539;

650 0 a| Kernel functions.=| ^A40027;

650 0 a| Surfaces, Algebraicx| Degenerations.=| ^A608984;

650 0 a| Surgery (Topology)=| ^A95312;

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;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Rochon, Frédéric,d| 1978-?| UNAUTHORIZED;

700 1 a| Sher, Davidq| (David A.),d| 1987-?| UNAUTHORIZED;

856 40 z| Full text available from Memoirs of the American Mathematical Societyu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Fwww.ams.org%2Fmemo%2F1314%2F;

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Resolvent, heat kernel, and torsion under degeneration to fibered cusps / Pierre Albin, Frédéric Rochon, David Sher.

Author/creator	Albin, Pierre, 1976-
Other author	Rochon, Frédéric, 1978-
Other author	Sher, David (David A.), 1987-
Format	Electronic
Publication Info	Providence, Rhode Island : American Mathematical Society, [2021]
Description	pages cm.
Supplemental Content	Full text available from Memoirs of the American Mathematical Society
Subjects	Riemannian manifolds. Symmetric spaces. Torsion theory (Algebra) Resolvents (Mathematics) Heat equation. Kernel functions. Surfaces, Algebraic--Degenerations. Surgery (Topology)

Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1314
Contents	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.
Abstract	"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.
General note	"January 2021, volume 269, number 1314 (fifth of 7 numbers)."
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2021016979
ISBN	9781470444228 (paperback)
ISBN	(pdf)

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Resolvent, heat kernel, and torsion under degeneration to fibered cusps / Pierre Albin, Frédéric Rochon, David Sher.

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