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@book{1398124,
author = {Bering Larsen, Klaus},
address = {Brno, Czech Republic},
keywords = {Supermathematics; Supermanifolds; Odd Poisson Geometry; Darboux Theorem; Antibracket; Batalin-Vilkovisky Geometry; Curvature;},
language = {eng},
location = {Brno, Czech Republic},
note = {Nepřenášet do RIV. jedná se o habilitační práci, která nesplňuje podmínku 50ti stran textu podle M17+.},
publisher = {Habilitation thesis, Masaryk University},
title = {Odd Scalar Curvature in Batalin-Vilkovisky Geometry},
year = {2017}
}
TY - BOOK
ID - 1398124
AU - Bering Larsen, Klaus
PY - 2017
TI - Odd Scalar Curvature in Batalin-Vilkovisky Geometry
PB - Habilitation thesis, Masaryk University
CY - Brno, Czech Republic
N1 - Nepřenášet do RIV. jedná se o habilitační práci, která nesplňuje podmínku 50ti stran textu podle M17+.
KW - Supermathematics
KW - Supermanifolds
KW - Odd Poisson Geometry
KW - Darboux Theorem
KW - Antibracket
KW - Batalin-Vilkovisky Geometry
KW - Curvature;
N2 - After a brief introduction to Batalin-Vilkovisky (BV) formalism, we treat aspects of supermathematics in algebra and differential geometry, such as, stratification theorems, Frobenius theorem and Darboux theorem on supermanifolds. We use Weinstein's splitting principle to prove Darboux theorem for regular, possible degenerate, even and odd Poisson supermanifolds. Khudaverdian's nilpotent operator (which takes semidensities into semidensities of opposite Grassmann-parity) is introduced on both (i) an atlas of Darboux coordinates and (ii) in arbitrary coordinates. An odd scalar function is defined and it is shown that it has a geometric interpretation as an odd scalar curvature.
ER -
BERING LARSEN, Klaus. \textit{Odd Scalar Curvature in Batalin-Vilkovisky Geometry}. Brno, Czech Republic: Habilitation thesis, Masaryk University, 2017, 36 s.
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