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Analytic torsion for twisted de Rham complexes 13:10 Fri 30 Oct 09 | School Board Room | Prof Mathai Varghese | University of Adelaide
Abstract... [19]We define analytic torsion for the twisted de Rham complex, consisting of differential forms on a compact Riemannian manifold X with coefficients in a flat vector bundle E, with a differential given by a flat connection on E plus a closed odd degree differential form on X. The definition in our case is more complicated than in the case discussed by Ray-Singer, as it uses pseudodifferential operators. We show that this analytic torsion is independent of the choice of metrics on X and E, establish some basic functorial properties, and compute it in many examples. We also establish the relationship of an invariant version of analytic torsion for T-dual circle bundles with closed 3-form flux. This is joint work with Siye Wu.
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Publications matching "Analytic torsion for twisted de Rham complexes"
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Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls
Larusson, Finnur; Sigurdsson, R, Mathematische Annalen 345 (159–174) 2009 |
Learning fuzzy rules with evolutionary algorithms - An analytic approach
Kroeske, Jens; Ghandar, Adam; Michalewicz, Zbigniew; Neumann, F, 10th International Conference on Parallel Problem Solving from Nature, Germany 01/09/08 |
Oriented bond percolation and phase transitions: an analytic approach
Pearce, Charles, International Conference on Numerical Analysis and Applied Mathematics, Corfu, Greece 16/09/07 |
Fractional analytic index
Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 74 (265–292) 2006 |
Heat kernels and the range of the trace on completions of twisted group algebras
Varghese, Mathai, Contemporary Mathematics 398 (321–345) 2006 |
Mathematical modelling of oxygen concentration in bovine and murine cumulus-oocyte complexes
Clark, Alys; Stokes, Yvonne; Lane, Michelle; Thompson, Jeremy, Reproduction 131 (999–1006) 2006 |
Methodology in meta-analysis: a study from critical care meta-analytic practice
Moran, John; Solomon, Patricia; Warn, D, Health Services and Outcomes Research Methodology 5 (207–226) 2006 |
An analytic modelling approach for network routing algorithms that use "ant-like" mobile agents
Bean, Nigel; Costa, Andre, Computer Networks-The International Journal of Computer and Telecommunications Networking 49 (243–268) 2005 |
L2 torsion without the determinant class condition and extended L2 cohomology
Braverman, M; Carey, Alan; Farber, M; Varghese, Mathai, Communications in Contemporary Mathematics 7 (421–462) 2005 |
Some relations between twisted K-theory and E8 gauge theory
Varghese, Mathai; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 3 (WWW 1–WWW 22) 2004 |
Second moments of a matrix analytic model of machine maintenance
Green, David; Metcalfe, Andrew, IMA International Conference on Modelling in Industrial Maintenance and Reliability (5th: 2004), Salford, United Kingdom 05/04/04 |
Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible
Roberts, Anthony John, SIAM Journal on Applied Dynamical Systems 3 (433–462) 2004 |
Some relations between twisted K-theory and E-8 gauge theory
Mathai, V; Sati, Hicham, The Journal of High Energy Physics (Online Editions) (WWW1–WWW22) 2004 |
Chern character in twisted K-theory: Equivariant and holomorphic cases
Varghese, Mathai; Stevenson, Daniel, Communications in Mathematical Physics 236 (161–186) 2003 |
Edge of the wedge theory in hypo-analytic manifolds
Eastwood, Michael; Graham, C, Communications in Partial Differential Equations 28 (2003–2028) 2003 |
Type-1 D-branes in an H-flux and twisted KO-theory
Varghese, Mathai; Murray, Michael; Stevenson, Daniel, The Journal of High Energy Physics (Online Editions) 11 (www 1–www 22) 2003 |
Nonclassical description of analytic cohomology
Bailey, T; Eastwood, Michael; Gindikin, S, |
A matrix analytic model for machine maintenance
Green, David; Metcalfe, Andrew; Swailes, D, Matrix-Analytic Methods: Theory and Applications, Adelaide, Australia 14/07/02 |
Twisted K-theory and K-theory of bundle gerbes
Bouwknegt, Pier; Carey, Alan; Varghese, Mathai; Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 228 (17–45) 2002 |
Flow in spiral channels of small curvature and torsion
Stokes, Yvonne, The IUTAM Symposium on Free Surface Flows, Birmingham, UK 10/07/00 |
Twisted index theory on good orbifolds, II: Fractional quantum numbers
Marcolli, M; Varghese, Mathai, Communications in Mathematical Physics 217 (55–87) 2001 |
Analytic continuation of vector bundles with Lp-curvature
Harris, A; Tonegawa, Y, International Journal of Mathematics 11 (29–40) 2000 |
Correspondences, von Neumann algebras and holomorphic L2 torsion
Carey, Alan; Farber, M; Varghese, Mathai, Canadian Journal of Mathematics-Journal Canadien de Mathematiques 52 (695–736) 2000 |
D-Branes, B-Fields and twisted K-theory
Bouwknegt, Pier; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (1–11) 2000 |
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