{"title":"Reinhardt-Martin Jane","description":null,"products":[{"product_id":"flax-your-way-to-better-health-book-reinhardt-martin-jane-9780971230408","title":"Flax Your Way to Better Health","description":"The theory of shadows of 3 and 4-manifolds represents a bridge between combinatorics of polyhedra and low-dimensional topology. On the one hand, it allows a purely combinatorial approach to the study of smooth 4-manifolds and, on the other, it indicates relations between old-standing problems in group theory and recent topological results on 4-dimensional manifolds. The present Ph.D. thesis is devoted to further develop these connections and to find new applications to low-dimensional topology. The results proved, for the most part, seem to strengthen the idea that topology of 3-manifolds can be used as a guide to study the 4-dimensional case and that polyhedra can be used as a bridge in many cases the 4-dimensional results based on shadows restrict through the theory of spines to results about 3-dimensional topology and geometry. On the 3-dimensional side, a new notion of shadow-complexity of 3-manifolds is defined. The study of this complexity clarifies how hyperbolic geometry of 3-manifolds is intimately connected with the combinatorial structure of the polyhedra used to describe the manifolds. On the 4-dimensional side, the notion of branched shadow is introduced in order to study, through a purely combinatorial approach, differentiable objects as Spinc and almost complex structures on smooth 4-manifolds. Combinatorial sufficient conditions based on these objects are proved assuring that refined structures on 4-manifolds exist such as integrable complex structures and Stein domain structures.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49514134438161,"sku":"GOR010707289","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":49990981222673,"sku":"CIN0971230404G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0971230404.jpg?v=1750705798"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-reinhardt-martin-jane.oembed","provider":"World of Books ","version":"1.0","type":"link"}