논문KCI 등재
MORSE INEQUALITIES FOR MANIFOLDS WITH BOUNDARY
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The aim of this paper is to provide a proof for a version of the Morse inequalities for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof for it. Our proof is analytic and is based on the J. Roe account of Witten’s approach to Morse Theory.
Abstract
The aim of this paper is to provide a proof for a version of the Morse inequalities for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof for it. Our proof is analytic and is based on the J. Roe account of Witten’s approach to Morse Theory.
참고문헌 (11)
- M. F. Atiyah, "Spectral asymmetry and Riemannian geometry", I, Math. Proc. Cambridge Philos. Soc., 통권 : 77, pp.43~69 (1975)
- N. Berline, ", 298" (1992), Springer-Verlag
- B. Booß-Bavnbek, "Elliptic Boundary Problems for Dirac Operators, Mathematics: Theory & Applications" (1993), Birkh¨auser Boston Inc.
- R. Bott, "Nondegenerate critical manifolds", Ann. of Math., 60(2), pp.248~261 (1954)
- P. B. Gilkey, "Asymptotic Formulae in Spectral Geometry, Studies in Advanced Mathematics", pp.2004, Chapman & Hall
- J. Milnor, "Morse Theory, Based on lecture notes, Annals of Mathematics Studies, No. 51" (1963), Princeton University Press
- J. Milnor, "Lectures on the h-Cobordism Theorem" (1965), Princeton University Press
- J. Roe, "Elliptic Operators, Topology and Asymptotic Methods, volume 395 of Pitman Research Notes in Mathematics Series" (1998), Longman
- M. E. Taylor, "Partial Differential Equations I, volume 115 of Applied Mathematical Sciences" (1996), Springer-Verlag
- E. Witten, "Supersymmetry and Morse theory", J. Differential Geom., 17(4), pp.661~692 (1982)
- W. Zhang, "Lectures on Chern-Weil Theory and Witten Deformations, volume 4 of Nankai Tracts in Mathematics" (2001), World Scientific Publishing Co. Inc.
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