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Notes on Seiberg-Witten theory

Domenii publicaţii > Matematica + Tipuri publicaţii > Carte

Autori: Liviu I. Nicolaescu

Editorial: American Mathematica Society, 2000.

Rezumat:

In aceasta carte prezentam in detaliu, si cu multe exemple, o colectzie de principii, tehnici si aplicatzii necesare in studii de teoria gauge si aplicatziile ei in geometrie si topologie. Cartea contzine calcule complete a invariantzilor Seiberg-Witten a marii majoritatzi de suprafetze algebrice simplu conexe, folosind doar metoda factorizarii a lui Witten. De asemenea prezentam o noua metoda de decupare si lipire a invariatzilor Seiberg-Witten pe care o ilustram prin exemple ca teorema sumei conexe, formaula de blow-up, teorema de anulare a lui Fintushel-Stern. In this volume we present, in great detail and with many examples, a basic collection of principles, techniques, and applications needed to conduct independent research in gauge theory and its use in geometry and topology. Complete and self-contained computations of the Seiberg-Witten invariants of most simply connected algebraic surfaces using only Witten’s factorization method are included. Also given is a new approach to cutting and pasting Seiberg-Witten invariants, which is illustrated by examples such as the connected sum theorem, the blow-up formula, and a proof of a vanishing result of Fintushel and Stern.

Cuvinte cheie: teorie gauge, geometrie, topologie // gauge theory, geometry, topology