Biomedical subjects

S E Cappell

Publications and source records attributed to S E Cappell.

2 recordsLinked to original sources

PubMed1987

Characteristic classes, singular embeddings, and intersection homology.

This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper.

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PubMed1980

Fixed points of periodic maps.

Let f be a periodic differentiable map from a sphere to itself. A well-known conjecture of Smith asserts that in many cases (e.g., when the fixed points are isolated) the derivatives of f at its fixed points, regarded as Jacobian matrices, are linearly similar. Here we give counterexamples to this conjecture. The results show that, in many cases, these Jacobian matrices are only nonlinearly similar. This uses our recent discovery of orthogonal matrices which are nonlinearly similar without being linearly similar. Some results on general smooth actions of finite groups on differentiable manifolds are presented; the topological equivalence of their tangential representations at the fixed points is studied.

Journal Article↗