A Geometric Approach to Homology Theory

The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories.

S. Buonchristiano (Author), C. P. Rourke (Author), B. J. Sanderson (Author)

9780521209403, Cambridge University Press

Paperback, published 1 April 1976

156 pages
23 x 15 x 1 cm, 0.24 kg

The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.

1. Homotopy functors
2. Mock bundles
3. Coefficients
4. Geometric theories
5. Equivariant theories and operations
6. Sheaves
7. The geometry of CW complexes.

Subject Areas: Geometry [PBM]