The Hodge Theory of Projective Manifolds by Mark Andrea A De Cataldo

By Mark Andrea A De Cataldo

This e-book is a written-up and elevated model of 8 lectures at the Hodge concept of projective manifolds. It assumes little or no historical past and goals at describing how the idea turns into gradually richer and extra appealing as one specializes from Riemannian, to Kähler, to complicated projective manifolds. notwithstanding the facts of the Hodge Theorem is passed over, its results topological, geometrical and algebraic are mentioned at a few size. The particular houses of complicated projective manifolds represent a tremendous physique of information and readers are guided via it with the aid of chosen workouts. regardless of beginning with only a few must haves, the concluding bankruptcy works out, within the significant distinct case of surfaces, the facts of a distinct estate of maps among complicated projective manifolds, which was once found in basic terms relatively lately.

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Differential topology: first steps by Andrew H. Wallace

By Andrew H. Wallace

Holding mathematical necessities to a minimal, this undergraduate-level textual content stimulates scholars' intuitive realizing of topology whereas heading off the tougher subtleties and technicalities. Its concentration is the strategy of round differences and the research of serious issues of capabilities on manifolds. 1968 version.

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Naive Lie Theory (Undergraduate Texts in Mathematics) by John Stillwell

By John Stillwell

During this new textbook, acclaimed writer John Stillwell provides a lucid creation to Lie idea appropriate for junior and senior point undergraduates. for you to accomplish that, he specializes in the so-called "classical groups'' that catch the symmetries of actual, complicated, and quaternion areas. those symmetry teams could be represented by way of matrices, which permits them to be studied via trouble-free equipment from calculus and linear algebra. This naive method of Lie conception is initially as a result of von Neumann, and it's now attainable to streamline it through the use of typical result of undergraduate arithmetic. To catch up on the constraints of the naive technique, finish of bankruptcy discussions introduce vital effects past these proved within the ebook, as a part of a casual caricature of Lie conception and its heritage. John Stillwell is Professor of arithmetic on the collage of San Francisco. he's the writer of numerous very hot books released by means of Springer, together with The 4 Pillars of Geometry (2005), components of quantity idea (2003), arithmetic and Its heritage (Second variation, 2002), Numbers and Geometry (1998) and components of Algebra (1994).

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Cohomology Theory of Topological Transformation Groups by Wu Yi Hsiang (auth.)

By Wu Yi Hsiang (auth.)

Historically, purposes of algebraic topology to the learn of topological transformation teams have been originated within the paintings of L. E. 1. Brouwer on periodic changes and, a bit later, within the appealing fastened aspect theorem ofP. A. Smith for top periodic maps on homology spheres. Upon evaluating the fastened element theorem of Smith with its predecessors, the fastened aspect theorems of Brouwer and Lefschetz, one unearths that it's attainable, at the least for the case of homology spheres, to improve the belief of mere lifestyles (or non-existence) to the particular choice of the homology kind of the fastened element set, if the map is thought to be top periodic. The pioneer results of P. A. Smith in actual fact indicates a fruitful basic path of learning topological transformation teams within the framework of algebraic topology. clearly, the fast difficulties following the Smith mounted aspect theorem are to generalize it either towards changing the homology spheres by means of areas of extra basic topological forms and towards changing the crowd tl by way of extra common compact groups.

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Metric rigidity theorems on Hermitian locally symmetric by Ngaiming Mok

By Ngaiming Mok

This monograph experiences the matter of characterizing canonical metrics on Hermitian in the community symmetric manifolds X of non-compact/compact forms by way of curvature stipulations. The proofs of those metric stress theorems are utilized to the research of holomorphic mappings among manifolds X of a similar variety. furthermore, a twin model of the generalized Frankel Conjecture on characterizing compact Kähler manifolds also are formulated.

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