Morse Theory
Algebraic Morse theory and homological perturbation theory
... discrete Morse theory in [For98] as a com- binatorial adaptation of the classical Morse theory suited for studying the topology of ...perturbation theory on the other hand builds on the ...
6
Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles
... Section 3 is the heart of the paper and contains the details of the Morse theory used to calculate the cohomology of the moduli space. The first result proves the isomorphism in Proposition 3.1. This is the ...
34
Embedded area constrained Willmore tori of small area in Riemannian three manifolds II : Morse Theory
... and Morse inequalities, for having existence/multiplicity of embedded tori which are stationary for the Willmore functional under the constraint of prescribed (sufficiently small) ...
49
Morse theory, Higgs fields, and Yang–Mills–Higgs functionals
... It is worth mentioning here the relationship with Palais’s work. The analytic details of the Morse theory for the Yang-Mills functional are slightly different than the cases studied in [46]. In particular, ...
39
Morse theory for the space of Higgs bundles
... of Morse theory in the spirit of Atiyah and Bott’s approach for holomor- phic bundles in [2] to compute topological invariants of these character varieties, a program that has been carried out for the case ...
46
Discrete Morse Theory & Persistent Homotopy
... discrete Morse function. It inherits a canonical irregular discrete Morse function with the same critical values as before, the sub-level sets of which are homotopy equivalent to the original ...
108
Multiple Solutions for Biharmonic Equations with Asymptotically Linear Nonlinearities
... on the nonlinear term f is not necessary, this point is very important because we can directly prove existence of positive solution and negative solution by using Rabinowitz’s mountain pass theorem. That is, the proof of ...
11
Cohomology of U(2,1) representation varieties of surface groups
... equivariant Morse theory techniques of Atiyah-Bott and Kirwan from [1] and [14] to the singular space of Higgs ...equivariant Morse function on the spaces of U (2, 1) Higgs bundles ...
36
Gradient systems with sublinear term near the origin and asymptotically linear term near infinity
... applying Morse theory to find critical points of is to compute critical groups both at infinity and at known critical points clearly and then to find unknown critical points by applying formulas ...
16
Multiple solutions for a fourth-order nonlinear elliptic problem which is superlinear at +∞ and linear at −∞
... We consider a semilinear fourth-order elliptic equation with a right-hand side nonlinearity which exhibits an asymmetric growth at + ∞ and at – ∞ . Namely, it is linear at – ∞ and superlinear at + ∞ . Combining ...
12
Category of Attractor and Its Application
... elementary Morse theory for an ...the Morse theory of attractors for semiflows on complete metric spaces by constructing continuous Lyapunov func- tions, and he introduced the concept of ...
5
Multiple solutions for a fourth-order nonlinear elliptic problem
... In this article, we consider multiple solutions of problem (1) in the non-resonance by using the mountain pass theorem and Morse theory. At first, we use the truncated skill and mountain pass theorem to ...
8
Existence of nontrivial solutions for a class of biharmonic equations with singular potential in \(\mathbb{R}^{N}\)
... In recent years, many authors have paid attention to studying the existence of nontrivial solutions for biharmonic equations (see, e.g., [1–3] and the references therein) since it was first introduced by Lazer and McKenna ...
14
Superlinear gradient system with a parameter
... a Morse theoretic ...methods, Morse theory and homological linking when is a saddle point in the sense that the parameter λ is very close to a higher eigenvalue of the related linear ...
17
Three Dimensional Manifolds All of Whose Geodesics Are Closed
... be free, the diagonal action of G on X × EG is always free, and the equivariant cohomology of X models the cohomology of X/G is the sense that for a free action we have H G ∗ (X; R) ∼ = H ∗ (X/G; R) . The negative ...
44
Existence of Multiple Solutions of a Second Order Difference Boundary Value Problem
... Although applications of the minimax methods in the field of the difference BVP have attracted some scholarly attention in the recent years, efforts in applying Morse theory to the difference BVP are scarce. ...
21
Bifurcations of transition states : morse bifurcations
... of Morse bifurcations, we were able to find interesting new transition states and dividing surfaces for the full non-collinear case, which has mostly been ignored until ...of Morse bifurcations, reduces to ...
39
Existence of solutions of elliptic boundary value problems with mixed type nonlinearities
... the existence of multiple nontrivial solutions for (P) are obtained by minimax methods and Morse theory.. It is well known that the (AR) condition is quite natural and convenient not onl[r] ...
11
Morse homology
... Morse theory has described how a compact finite dimensional manifold M is homotopy equivalent to a CW ...only Morse function is not enough to accomplish this, and we also need a transversality ...
71
Multiplicity of positive solutions for fractional elliptic systems involving sign-changing weight
... Discussion In recent years, there are many papers considering the relationship between the number of positive solutions of the elliptic equation and the topology of the global maximum set of its weight potentials. Our ...
23