000			02025 a2200241 4500
008			240418b |||||||| |||| 00| 0 eng d
020			_a9781470474287
082			_a516.362 CHO
100			_aChow, Bennett
245			_aRicci solitons in low dimensions
260			_aProvidence, Rhode Island: _bAmerican Mathematical Society, _c2023.
300			_axvi,339p.: _bhbk.: _c25cm
440			_a Graduate Studies in Mathematics Series, Vol.235
504			_aIncludes bibliography & index
520			_aRicci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifold's topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons. This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions. A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons. https://bookstore.ams.org/view?ProductCode=GSM/235
650			_a Global Differential Geometry
650			_aSolitons
650			_aRicci Flow Riemannian
650			_aGRS
650			_aMathematics
650			_aGeometric
942			_cTD _2ddc
999			_c59547 _d59547