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Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n national, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, finding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 the orbit space of the free circle action S /S =CP = S .

Homotopy theory. --- Invariants. --- Deformations, Continuous --- Topology --- Algebraic topology. --- Algebraic Topology.

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Ordered algebraic structures --- Cobordism theory --- Homotopy theory --- K-theory --- Algebraic topology --- Homology theory --- Deformations, Continuous --- Topology --- Differential topology --- Cobordism theory. --- Homotopy theory. --- K-theory. --- K-théorie. --- Homotopie. --- Cobordismes, Théorie des.

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Explicit Brauer Induction is an important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this 1994 book it is derived algebraically, following a method of R. Boltje - thereby making the technique, previously topological, accessible to algebraists. Once developed, the technique is used, by way of illustration, to re-prove some important known results in new ways and to settle some outstanding problems. As with Brauer's original result, the canonical formula can be expected to have numerous applications and this book is designed to introduce research algebraists to its possibilities. For example, the technique gives an improved construction of the Oliver-Taylor group-ring logarithm, which enables the author to study more effectively algebraic and number-theoretic questions connected with class-groups of rings.

Brauer groups. --- Representations of groups.

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Algebraic topology --- topologie (wiskunde)

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Bioceramics: Properties, Characterizations, and Applications is a general introduction to the uses of ceramics and glasses in the human body for the purposes of aiding, healing, correcting deformities, and restoring lost function. With over 35 years experience, the author developed the text as an outgrowth of a course for senior and beginning graduate students in biomedical engineering and will emphasize the fundamentals and applications in modern implant fabrication, and will also deal with tissue engineering scaffolds made of ceramics. Organized as a textbook for the student needing to acquire the core competencies, it will meet the demands of advanced undergraduate or graduate coursework in bioceramics, biomaterials, biomedical engineering, and biophysics. Key Features:  Detailed illustrations  Example problems to provide the student with hands-on experience with concepts  Extensive appendices and tutorial materials on new developments including expanded treatment of ceramic materials and implants  Tissue engineering and regenerative medicine  Detailed references for further reading About the Author: Joon Park is a Professor in the Biomedical Engineering Department at the College of Engineering at the University of Iowa.

Engineering. --- Biomedical Engineering. --- Biomaterials. --- Biophysics/Biomedical Physics. --- Ceramics, Glass, Composites, Natural Methods. --- Surfaces and Interfaces, Thin Films. --- Biomedical engineering. --- Surfaces (Physics). --- Ingénierie --- Génie biomédical --- Surfaces (Physique) --- Biomedical materials. --- Ceramics in medicine. --- Ceramics in medicine --- Biomedical materials --- Health & Biological Sciences --- Biomedical Engineering --- Biocompatible materials --- Biomaterials --- Medical materials --- Medicine --- Materials --- Biophysics. --- Biological physics. --- Industrial engineering. --- Production engineering. --- Thin films. --- Industrial and Production Engineering. --- Biophysics and Biological Physics. --- Surfaces. --- Films, Thin --- Solid film --- Solid state electronics --- Solids --- Surfaces (Technology) --- Coatings --- Thick films --- Surface phenomena --- Friction --- Surfaces (Physics) --- Tribology --- Biomedical engineering --- Biocompatibility --- Prosthesis --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Manufacturing engineering --- Process engineering --- Industrial engineering --- Mechanical engineering --- Management engineering --- Simplification in industry --- Value analysis (Cost control) --- Biological physics --- Biology --- Medical sciences --- Physics --- Construction --- Industrial arts --- Technology --- Surfaces --- Algebraic topology --- Congresses. --- Congresses --- Topologie algébrique --- Congrès --- Biomedical Engineering and Bioengineering. --- Biological and Medical Physics, Biophysics. --- Ceramics, Glass, Composites, Natural Materials. --- Surface chemistry --- Ceramics. --- Glass. --- Composites (Materials). --- Composite materials. --- Materials—Surfaces. --- Bioartificial materials --- Hemocompatible materials --- Composites (Materials) --- Multiphase materials --- Reinforced solids --- Solids, Reinforced --- Two phase materials --- Amorphous substances --- Ceramics --- Glazing --- Ceramic technology --- Industrial ceramics --- Keramics --- Building materials --- Chemistry, Technical --- Clay --- Biomaterials (Biomedical materials) --- Topologie algébrique