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21	On Partial Regularities and Monomial Preorders Nguyen, Thi Van Anh 28 June 2018 (has links) My PhD-project has two main research directions. The first direction is on partial regularities which we define as refinements of the Castelnuovo-Mumford regularity. Main results are: relationship of partial regularities and related invariants, like the a-invariants or the Castelnuovo-Mumford regularity of the syzygy modules; algebraic properties of partial regularities via a filter-regular sequence or a short exact sequence; generalizing a well-known result for the Castelnuovo-Mumford regularity to the case of partial regularities of stable and squarefree stable monomial ideals; finally extending an upper bound proven by Caviglia-Sbarra to partial regularities. The second direction of my project is to develop a theory on monomial preorders. Many interesting statements from the classical theory of monomial orders generalize to monomial preorders. Main results are: a characterization of monomial preorders by real matrices, which extends a result of Robbiano on monomial orders; secondly, leading term ideals with respect to monomial preorders can be studied via flat deformations of the given ideal; finally, comparing invariants of the given ideal and the leading term ideal with respect to a monomial preorder. 31.23 - Ideale, Ringe, Moduln, Algebren 13-02 - Research exposition ddc:510
22	l<sup>p</sup>-Kohomologie, insbesondere Verschwindungssätze für l<sup>p</sup>-Kohomologie / l<sup>p</sup>-cohomology, in particular vanishing theorems for l<sup>p</sup>-cohomology Kappos, Elias 10 July 2007 (has links) No description available. 510 Mathematik Mathematics and Computer Science lp-Kohomologie diskrete Gruppen Gruppen vom Typ FPn lp-Bettizahlen lp-cohomology diskrete groups groups of type FPn lp-Betti numbers 31.61 31.21
23	Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture / Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture Knebusch, Anselm 19 October 2009 (has links) No description available. 510 Mathematik EEGL 000 Selfadjoint operator algebras EEGM 200 Methods of algebraic topology Mathematics and Natural Science Betti-Zahlen von Neumann-Algebren Operatortheorie G-CW-Komplex Approximation Atiyah Vermutung Betti-numbers von Neumann-algebras operatortheory G-CW-complex approximation Atiyah conjecture 31.55 Globale Analysis 31.47 Operatortheorie

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