Normale Ansicht MARC ISBD

Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck Jean-Michel Bismut, Shu Shen, Zhaoting Wei

Von:

Bismut, Jean-Michel, 1948- [VerfasserIn]

Mitwirkende(r):

Materialtyp: Text

TextSprache: Englisch Reihen: Progress in mathematics ; 347Verlag: Cham Birkhäuser [2023]Beschreibung: x, 184 Seiten 25 cmInhaltstyp:

Text

Medientyp:

ohne Hilfsmittel zu benutzen

Datenträgertyp:

Band

ISBN:

9783031272332

Schlagwörter:

Andere physische Formen: Kein Titel; Erscheint auch als: Coherent Sheaves, Superconnections, and Riemann-Roch-GrothendieckAndere Klassifikation:

31.61
31.27

Online-Ressourcen:

zbMATH Review

Zusammenfassung: Publisher’s description: This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian. Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.

Exemplare ( 1 )
Titelinformationen ( 2 )

Exemplare
Medientyp	Aktuelle Bibliothek	Sammlung	Standort	Signatur	Status	Fälligkeitsdatum	Barcode
Buch	Gebäude E2 3 (UdS Campusbibliothek für Informatik und Mathematik)	Campusbibliothek für Informatik und Mathematik (E2 3)	Series (B)	PM 347 (Regal durchstöbern(Öffnet sich unterhalb))	Verfügbar		2203000150210

Regale von HOMEBRANCH: Universität des Saarlandes Fachrichtung Mathematik durchstöbern, Standort: Series (B), Sammlung: Campusbibliothek für Informatik und Mathematik (E2 3) Regalbrowser ausblenden (Regal ausblenden)

Zurück								Weiter
Zurück	PM 344 Singular integral operators, quantitative flatness, and boundary problems	PM 345 Mirzakhani's curve counting and geodesic currents	PM 346 Boundary value problems and Hardy spaces for elliptic systems with block structure	PM 347 Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck	PM 348 Isoperimetric inequalities in Riemannian manifolds	PM 349 Noncommutative integration and operator theory	PM 35 Arithmetic and geometry 1 Arithmetic	Weiter

Literaturverzeichnis: Seite 175-177

Publisher’s description: This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian. Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.