The Geometry of Supermanifolds

The Geometry of Supermanifolds

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'Et moi, ...* si favait III mmment en revenir, One service mathematics has rendered the je n'y serais point aile:' human race. It has put CXlUImon sense back Iules Verne where it belongs. on the topmost shelf next to the dUlty canister lahelled 'discarded non- The series i. divergent; therefore we may be able to do something with it. Eric T. Bell O. Hesvi.ide Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d't!tre of this series.
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Product details

  • Hardback | 242 pages
  • 155 x 235 x 16mm | 1,220g
  • Dordrecht, Netherlands
  • English
  • 1991 ed.
  • XIX, 242 p.
  • 0792314409
  • 9780792314400

Table of contents

I: Foundations.- I - Elements of graded algebra.- 1. Graded algebraic structures.- 2. Graded algebras and graded tensor calculus.- 3. Matrices.- II - Sheaves and cohomology.- 1. Presheaves and sheaves.- 2. Sheaf cohomology.- 3. de Rham, Dolbeault, and ?ech cohomologies.- 4. Graded Ringed spaces.- II Supermanifolds.- III - Categories of supermanifolds.- 1. Graded manifolds.- 2. Supersmooth functions.- 3. GH? functions.- 4. G-supermanifolds.- IV - Basic geometry of G-supermanifolds.- 1. Morphisms.- 2. Products.- 3. Super vector bundles.- 4. Graded exterior differential calculus.- 5. Projectable graded vector fields.- 6. DeWitt supermanifolds.- 7. Rothstein's axiomatics.- V - Cohomology of supermanifolds.- 1. de Rham cohomology of graded manifolds.- 2. Cohomology of graded differential forms.- 3. Cohomology of DeWitt supermanifolds.- 4. Again on the structure of DeWitt supermanifolds.- VI - Geometry of super vector bundles.- 1. Connections.- 2. Super line bundles.- 3. Characteristic classes.- 4. Characteristic classes in terms of curvature forms.- VII - Lie supergroups and principal super fibre bundles.- 1. Lie supergroups.- 2. Lie supergroup actions.- 3. Principal superfibre bundles.- 4. Connections.- 5. Associated super fibre bundles.
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