Hypoelliptic Laplacian and Bott-Chern cohomology: a theorem of Riemann-Roch-Grothendieck in complex geometry
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
2013
|
| Schriftenreihe: | Progress in mathematics
305 |
| Links: | https://doi.org/10.1007/978-3-319-00128-9 https://doi.org/10.1007/978-3-319-00128-9 https://doi.org/10.1007/978-3-319-00128-9 https://doi.org/10.1007/978-3-319-00128-9 https://doi.org/10.1007/978-3-319-00128-9 https://doi.org/10.1007/978-3-319-00128-9 https://doi.org/10.1007/978-3-319-00128-9 https://doi.org/10.1007/978-3-319-00128-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026059697&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026059697&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 1 Online-Ressource |
| ISBN: | 9783319001272 9783319001289 |
| DOI: | 10.1007/978-3-319-00128-9 |
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Datensatz im Suchindex
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| adam_text | HYPOELLIPTIC LAPLACIAN AND BOTT–CHERN COHOMOLOGY
/ BISMUT, JEAN-MICHEL
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
1 THE RIEMANNIAN ADIABATIC LIMIT
2 THE HOLOMORPHIC ADIABATIC LIMIT
3 THE ELLIPTIC SUPERCONNECTIONS
4 THE ELLIPTIC SUPERCONNECTION FORMS
5 THE ELLIPTIC SUPERCONNECTIONS FORMS
6 THE HYPOELLIPTIC SUPERCONNECTIONS
7 THE HYPOELLIPTIC SUPERCONNECTION FORMS
8 THE HYPOELLIPTIC SUPERCONNECTION FORMS OF VECTOR BUNDLES
9 THE HYPOELLIPTIC SUPERCONNECTION FORMS
10 THE EXOTIC SUPERCONNECTION FORMS OF A VECTOR BUNDLE
11 EXOTIC SUPERCONNECTIONS AND RIEMANN–ROCH–GROTHENDIECK
BIBLIOGRAPHY
SUBJECT INDEX
INDEX OF NOTATION.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
HYPOELLIPTIC LAPLACIAN AND BOTT–CHERN COHOMOLOGY
/ BISMUT, JEAN-MICHEL
: 2013
ABSTRACT / INHALTSTEXT
THE BOOK PROVIDES THE PROOF OF A COMPLEX GEOMETRIC VERSION OF A
WELL-KNOWN RESULT IN ALGEBRAIC GEOMETRY: THE THEOREM OF
RIEMANN–ROCH–GROTHENDIECK FOR PROPER SUBMERSIONS. IT GIVES AN
EQUALITY OF COHOMOLOGY CLASSES IN BOTT–CHERN COHOMOLOGY, WHICH IS A
REFINEMENT FOR COMPLEX MANIFOLDS OF DE RHAM COHOMOLOGY. WHEN THE
MANIFOLDS ARE KAEHLER, OUR MAIN RESULT IS KNOWN. A PROOF CAN BE GIVEN
USING THE ELLIPTIC HODGE THEORY OF THE FIBRES, ITS DEFORMATION VIA
QUILLEN S SUPERCONNECTIONS, AND A VERSION IN FAMILIES OF THE FANTASTIC
CANCELLATIONS OF MCKEAN–SINGER IN LOCAL INDEX THEORY. IN THE GENERAL
CASE, THIS APPROACH BREAKS DOWN BECAUSE THE CANCELLATIONS DO NOT OCCUR
ANY MORE.ONE TOOL USED IN THE BOOK IS A DEFORMATION OF THE HODGE
THEORY OF THE FIBRES TO A HYPOELLIPTIC HODGE THEORY, IN SUCH A WAY THAT
THE RELEVANT COHOMOLOGICAL INFORMATION IS PRESERVED, AND FANTASTIC
CANCELLATIONS DO OCCUR FOR THE DEFORMATION. THE DEFORMED HYPOELLIPTIC
LAPLACIAN ACTS ON THE TOTAL SPACE OF THE RELATIVE TANGENT BUNDLE OF
THE FIBRES. WHILE THE ORIGINAL HYPOELLIPTIC LAPLACIAN DISCOVERED BY THE
AUTHOR CAN BE DESCRIBED IN TERMS OF THE HARMONIC OSCILLATOR ALONG THE
TANGENT BUNDLE AND OF THE GEODESIC FLOW, HERE, THE HARMONIC OSCILLATOR
HAS TO BE REPLACED BY A QUARTIC OSCILLATOR.ANOTHER IDEA DEVELOPED IN
THE BOOK IS THAT WHILE CLASSICAL ELLIPTIC HODGE THEORY IS BASED ON THE
HERMITIAN PRODUCT ON FORMS, THE HYPOELLIPTIC THEORY INVOLVES A HERMITIAN
PAIRING WHICH IS A MILD MODIFICATION OF INTERSECTION PAIRING.
PROBABILISTIC CONSIDERATIONS PLAY AN IMPORTANT ROLE, EITHER AS A
MOTIVATION OF SOME CONSTRUCTIONS, OR IN THE PROOFS THEMSELVES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| author | Bismut, Jean-Michel 1948- |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512.66 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-00128-9 |
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| language | English |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Bismut, Jean-Michel 1948- Hypoelliptic Laplacian and Bott-Chern cohomology a theorem of Riemann-Roch-Grothendieck in complex geometry Progress in mathematics |
| title | Hypoelliptic Laplacian and Bott-Chern cohomology a theorem of Riemann-Roch-Grothendieck in complex geometry |
| title_auth | Hypoelliptic Laplacian and Bott-Chern cohomology a theorem of Riemann-Roch-Grothendieck in complex geometry |
| title_exact_search | Hypoelliptic Laplacian and Bott-Chern cohomology a theorem of Riemann-Roch-Grothendieck in complex geometry |
| title_full | Hypoelliptic Laplacian and Bott-Chern cohomology a theorem of Riemann-Roch-Grothendieck in complex geometry Jean-Michel Bismut |
| title_fullStr | Hypoelliptic Laplacian and Bott-Chern cohomology a theorem of Riemann-Roch-Grothendieck in complex geometry Jean-Michel Bismut |
| title_full_unstemmed | Hypoelliptic Laplacian and Bott-Chern cohomology a theorem of Riemann-Roch-Grothendieck in complex geometry Jean-Michel Bismut |
| title_short | Hypoelliptic Laplacian and Bott-Chern cohomology |
| title_sort | hypoelliptic laplacian and bott chern cohomology a theorem of riemann roch grothendieck in complex geometry |
| title_sub | a theorem of Riemann-Roch-Grothendieck in complex geometry |
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