| Softcover ISBN: | 978-2-85629-993-7 |
| Product Code: | AST/450 |
| List Price: | $81.00 |
| AMS Member Price: | $64.80 |
| Softcover ISBN: | 978-2-85629-993-7 |
| Product Code: | AST/450 |
| List Price: | $81.00 |
| AMS Member Price: | $64.80 |
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Book DetailsAstérisqueVolume: 450; 2024; 482 ppMSC: Primary 57; 58; 81
This book shows that counting or computing the small eigenvalues of the Witten Laplacian in the semi-classical limit can be done without assuming, as the authors did in a previous article, that the potential is a Morse function .
In connection with persistent cohomology, the authors prove that the rescaled logarithms of these small eigenvalues are asymptotically determined by the lengths of the bar code of the potential function. In particular, this proves that these quantities are stable in the uniform convergence topology of the space of continuous functions. Additionally, the authors' analysis provides a general method for computing the subexponential corrections in a large number of cases.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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This book shows that counting or computing the small eigenvalues of the Witten Laplacian in the semi-classical limit can be done without assuming, as the authors did in a previous article, that the potential is a Morse function .
In connection with persistent cohomology, the authors prove that the rescaled logarithms of these small eigenvalues are asymptotically determined by the lengths of the bar code of the potential function. In particular, this proves that these quantities are stable in the uniform convergence topology of the space of continuous functions. Additionally, the authors' analysis provides a general method for computing the subexponential corrections in a large number of cases.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
