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040			_aP5A _cP5A
090			_atimpa
100	1		_aAgüero, Dan _9685
245	1	0	_aComplex Dirac structures with constant real index/ _cDan Agüero.
246	1	1	_aEstruturas de Dirac complexas com índice real constante.
260			_aRio de Janeiro: _bIMPA, _c2020.
300			_avideo online
500			_aBanca examinadora: Henrique Bursztyn - Orientador - IMPA Roberto Rubio - Coorientador - Univ. Autonoma de Barcelona Reimundo Heluani - IMPA Cristian Ortiz - USP Alejandro Cabrera - UFRJ Thiago Linhares - Suplente - UFRJ.
505	1		_aAbstract: This thesis studies complex Dirac structures (i.e., Dirac structures in the complexification of the generalized tangent bundle of a manifold) with constant real index. These objects extend generalized complex structures, which arise when the real index is zero, and encode geometric structures such as presymplectic, transverse holomorphic and CR structures. We introduce a new invariant that we call order, which is an nonnegative integer that allows us to obtain a classification of complex Dirac structures at the linear-algebraic level. We prove that complex Dirac structures with constant real index and order carry a presymplectic foliation which comes from an underlying (real) Dirac structure (generalizing the Poisson structures associated with generalized complex structures). We prove a local splitting theorem for complex Dirac structures with constant real index and order which extends the Abouzaid-Boyarchenko's splitting theorem for generalized complex structures. Finally we focus on complex Dirac structures with real index one; we study a pairing , analogous to the Chevalley-Mukai pairing, which gives information about the dimension of the intersection of the annihilators of two pure spinors. We use it to give a spinorial description of complex Dirac structure with real index one .
650	0	4	_aMatematica. _2larpcal _919899
697			_aTeses do IMPA _924311
700	1		_aBursztyn, Henrique. _u(IMPA, Brazil) _eorientador _92937
700	1		_aRubio, Roberto _u(Universidade Autonoma de Barcelona, Espanha) _eco-orientador _98531
700	1		_aHeluani, Reimundo. _u(IMPA, Brazil) _94335
700	1		_aOrtiz, Cristian _u(USP, Brazil) _9361
700	1		_aCabrera, Alejandro _u(UFRJ, Brazil) _96487
700	1		_aLinhares, Thiago _u(UFRJ, Brazil) _9686
711	2		_aDefesa de Tese _910070
856	4		_zVIDEO _uhttps://youtu.be/zge-0o6y5xE
942			_2ddc _cBK
999			_aCOMPLEX Dirac structures with constant real index. Dan Agüero. Rio de Janeiro: IMPA, 2020. video online. Disponível em: <https://youtu.be/zge-0o6y5xE>. Acesso em: 12 ago. 2020. _c38305 _d38305