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Topic: Lefschetz number

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	Hairy ball theorem - Wikipedia, the free encyclopedia
		Since the Betti numbers of a 2-sphere are 1, 0, 1, 0, 0,...
		the Lefschetz number (total trace on homology) of the identity mapping is 2.
		The difference in even and odd dimension is that the Betti numbers of the m-sphere are 0 except in dimensions 0 and m.
	en.wikipedia.org /wiki/Hairy_ball_theorem (868 words)

	Papers and Articles: Daniel Henry Gottlieb
		(with J. Becker and Andrew Casson) The Lefschetz number and fibre preserving maps.
		A Gravitational Lens Need Not Produce an Odd Number of Images.
		Proceedings of the 7th Marcel Grossman Relativity Conference on Relativity,
	www.math.purdue.edu /~gottlieb/Bibliography/bib.html (548 words)

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