02503nam a22004215i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184082001500207100003100222245010500253264007500358300004300433336002600476337002600502338003600528347002400564490005300588505017100641520089500812650001701707650003701724650003401761650001701795650002701812650005101839710003401890773002001924776003601944830005301980856004802033978-3-319-02441-7DE-He21320150803155057.0cr nn 008mamaa131121s2014 gw | s |||| 0|eng d a97833190244177 a10.1007/978-3-319-02441-72doi 4aQA641-670 7aPBMP2bicssc 7aMAT0120302bisacsh04a516.362231 aAngella, Daniele.eauthor.10aCohomological Aspects in Complex Non-Kähler Geometryh[electronic resource] /cby Daniele Angella. 1aCham :bSpringer International Publishing :bImprint: Springer,c2014. aXXV, 262 p. 7 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aLecture Notes in Mathematics,x0075-8434 ;v20950 aPreliminaries on (almost-) complex manifolds -- Cohomology of complex manifolds -- Cohomology of nilmanifolds -- Cohomology of almost-complex manifolds -- References. aIn these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered. 0aMathematics. 0aDifferential equations, partial. 0aGlobal differential geometry.14aMathematics.24aDifferential Geometry.24aSeveral Complex Variables and Analytic Spaces.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783319024400 0aLecture Notes in Mathematics,x0075-8434 ;v209540uhttp://dx.doi.org/10.1007/978-3-319-02441-7