By Liviu Nicolaescu

ISBN-10: 146141105X

ISBN-13: 9781461411055

This self-contained remedy of Morse thought specializes in functions and is meant for a graduate direction on differential or algebraic topology. The ebook is split into 3 conceptually specified components. the 1st half includes the rules of Morse conception. the second one half includes functions of Morse thought over the reals, whereas the final half describes the fundamentals and a few purposes of advanced Morse concept, a.k.a. Picard-Lefschetz theory.

This is the 1st textbook to incorporate subject matters akin to Morse-Smale flows, Floer homology, min-max thought, second maps and equivariant cohomology, and complicated Morse concept. The exposition is more desirable with examples, difficulties, and illustrations, and should be of curiosity to graduate scholars in addition to researchers. The reader is anticipated to have a few familiarity with cohomology concept and with the differential and indispensable calculus on delicate manifolds.

Some positive aspects of the second one variation contain additional purposes, reminiscent of Morse concept and the curvature of knots, the cohomology of the moduli area of planar polygons, and the Duistermaat-Heckman formulation. the second one variation additionally encompasses a new bankruptcy on Morse-Smale flows and Whitney stratifications, many new routines, and diverse corrections from the 1st variation.

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**Additional info for An Invitation to Morse Theory (2nd Edition) (Universitext)**

**Example text**

44 Robert L. Blair [18] K. Hardy, Notes on two generalizations of almost realcom- pact spaces, Math. Centrum Amsterdam Afd. , ZW 57/75, 1975, 11 pp. [19] I. Juhâsz, Cardinal functions in topology, Math. Centre Tracts 34, Math. Centrum, Amsterdam, 1971. [20] _, K. Kunen, and M. E. Rudin, Two more separable non-Lindelof spaces, [21] M. Katetov, Measures in fully hereditarily to appear. normal spaces, Fund. Math. 38 (1951), 73-84. [22] J. Mack, On a class of countably paracompact spaces, Proc. Amer.

If X is L , then the following are equivalent: (a) X is closed-complete. (b) Every closed discrete subset of X has nonmeasurable power, and if F is any free closed ultrafilter on X, then {X - F:F ε F} has an open weak θ-refinement. Proof. 1 and (part of) the proof of the theorem of [36]. (a) => (b). e. 2]. closed ultrafilter on Moreover, if F is a free X, then, by (a), there is a sequence Set-Theoretic Topology 31 (F ) ΛΤ of members of F with n XTF = 0. ClearlyJ ^ η^ηεΝ ηεΝ n uηεΝ„{X - Fn } is an open weak θ-refinement of {X - F:F ε F}.

Math. 33 (1970), 571-581. [13] Z. Frolik_, Realcompaotness is a Baire-measurable property, Bull. Acad. Polon. Sei. Ser. Sei. Math. Astronom. Phy. 19 (1971), 617-621. [14] R. J. Gardner, The regularity of Borel measures and measure-compactness, Proc. London Math. Soc. (3) 20 (1975), 95-113. [15] L. Gillman and M. , Van Nostrand, Princeton, N. , 1960. [16] R. F. Gittings, On covering spaces, 43 topologioal and countable Canad. J. , Vol. 378, SpringerVerlag, Berlin-Heidelberg-New York, 1974, pp. 645-648.

### An Invitation to Morse Theory (2nd Edition) (Universitext) by Liviu Nicolaescu

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