Topology Crump

Hyperion presents a second volume of music from the Conductus repertory - the least-known genre of medieval music - performed by tenors John Potter, Christopher O'Gorman, Rogers Covey-Crump, three singers who combine expert knowledge of the music with voices of unearthly beauty. This album contains poems set to music from thirteenth-century England and France. The subjects range from straightforward exhortations to the Virgin Mary to criticisms of the Papal Curia and a depiction of the student riots in Orleans in 1236.

John Dowland (1563–1626) was an English Renaissance composer, lutenist, and singer. He is best known today for his melancholy songs such as "Come, heavy sleep" (the basis of Benjamin Britten's 1963 composition for solo guitar, Nocturnal after John Dowland), "Come again", "Flow my tears", "I saw my Lady weepe" and "In darkness let me dwell", but his instrumental music has undergone a major revival, and with the 20th century's early music revival, has been a continuing source of repertoire for lutenists and classical guitarists. Dowland published his The First Booke of Songes or Ayres in London in 1597. It was one of the most influential and important musical publications of the history of the lute. This collection of lute-songs was set out in a way that allows performance by a soloist with lute accompaniment or various combinations of singers and instrumentalists.

Topology is one of the fundamental tools in relating entities. Topology naturally finds application in all fields of engineering, physical sciences, life sciences, social sciences, medicine, business and even the arts. The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. Circa 1750, Euler stated the polyhedron formula, V − E + F = 2 (where V, E, and F respectively indicate the number of vertices, edges, and faces of the polyhedron), which may be regarded as the first theorem, signaling the birth of topology. Subjects included in topology are algebraic topology and graph theory. A related branch to graph theory is molecular topology (with concerns of either chemical or biological structure).

The essentials of point-set topology, complete with motivation and numerous examples
Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors.

This volume of the Encyclopaedia consists of two independent parts. The first contains a survey of results related to the concept of compactness in general topology. It highlights the role that compactness plays in many areas of general topology. The second part is devoted to homology and cohomology theories of general spaces. Special emphasis is placed on the method of sheaf theory as a unified approach to constructions of such theories. Both authors have succeeded in presenting a wealth of material that is of interest to students and researchers in the area of topology. Each part illustrates deep connections between important mathematical concepts. Both parts reflect a certain new way of looking at well known facts by establishing interesting relationships between specialized results belonging to diverse areas of mathematics.

This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field.

This book constitutes nothing less than an up-to-date survey of the whole field of topology (with the exception of "general (set-theoretic) topology"), or, in the words of Novikov himself, of what was termed at the end of the 19th century "Analysis Situs", and subsequently diversified into the various subfields of combinatorial, algebraic, differential, homotopic, and geometric topology. The book gives an overview of these subfields, beginning with the elements and proceeding right up to the present frontiers of research.

This book discusses various concepts and theories of topology, including diffeomorphisms, immersions, Hausdorff spaces, cobordisms, homotopy theory, symplectic manifolds, topology of quantum field theory, algebraic varieties, dimension theory, Koszul complexes, continuum theory, and metrizability, among others.