Antiperfect morse stratification

Antiperfect Morse Stratification Nan-kuo Ho and Chiu-chu

For an equivariant Morse stratification which contains a unique open stratum, we introduce the notion of equivariant antiperfection, which means the difference of the equivariant Morse series and the equivariant Poincaré series achieves the maximal possible value (instead of the minimal possible value 0 in the equivariantly perfect case). We also introduce a weaker condition of local equivarian...

Refinements of the Morse stratification of the normsquare of the moment map

Let X be any nonsingular complex projective variety with a linear action of a complex reductive group G, and let X and X be the sets of semistable and stable points of X in the sense of Mumford’s geometric invariant theory [17]. We can choose a maximal compact subgroup K of G and an inner product on the Lie algebra k of K which is invariant under the adjoint action. Then X has a G-equivariantly...

Morse Homology

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Morse Theory

On the stratification of a compact 3-manifold by the trajectroy spaces of a Morse-Smale flow

We consider a Morse function f and a Morse-Smale gradient-like vector field X on a compact connected oriented 3-manifold M such that f has only one critical point of index 3. Based on Laudenbach’s ideas [1], we will show that the flow of X can be isotoped into one so that the trajectory spaces of the new flow provide a stratification for M . We will construct ”natural” tubular neighborhoods abo...