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Author Harvey, F. Reese ♦ Lawson, H. Blaine
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Morse Theory ♦ Stokes Theorem ♦ Boundary Consisting ♦ Finite Complex ♦ Chain Homotopy ♦ Critical Point ♦ Stable Manifold ♦ Exterior Form Ff ♦ Sum P2cr ♦ Operator Equation Ffi Ffi ♦ Delta Gamma ♦ Diagonal Delta ♦ Chain Map ♦ Unstable Manifold ♦ Theta Sp ♦ Product Theta ♦ Interesting Application ♦ Intrinsic Approach ♦ Morse Function
Abstract We present a new, intrinsic approach to Morse Theory which has interesting applications in geometry. We show that a Morse function f on a manifold determines a submanifold T of the product X \Theta X, and that (in the sense that Stokes theorem is valid) T has boundary consisting of the diagonal \Delta ae X \Theta X and a sum P = X p2Cr(f) Up \Theta Sp where Sp and Up are the stable and unstable manifolds at the critical point p. In the language of currents, @T = \Delta \Gamma P:(Stokes Theorem) This current (or kernel) equation on X \Theta X is equivalent to an operator equation d ffi T+T ffi d = I \Gamma P; ((Chain Homotopy)) where P is a chain map onto the finite complex of currents S f spanned by (integration over) the stable manifolds of f . The operator P can be defd on an exterior form ff by P(ff) = lim t!1 '
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study