On closed 4-manifolds admitting a Morse function with 4 critical points

Surgery on Closed 4-manifolds with Free Fundamental Group

The 4-dimensional topological surgery conjecture has been established for a class of groups, including the groups of subexponential growth (see [6], [13] for recent developments), however the general case remains open. The full surgery conjecture is known to be equivalent to the question for a class of canonical problems with free fundamental group [5, Chapter 12]. The proof of the conjecture f...

Quaternionic Contact Manifolds with a Closed Fundamental 4-form

We define a global horizontal 4-form on a quaternionic contact manifold and show that it is closed if and only if the torsion of the Biquard connection vanishes provided the dimension is grater than seven. This condition characterizes quaternionic contact structures which are locally qc homothetic to 3-sasakian.

MATHEMA TICS: M. MORSE THE CRITICAL POINTS OF A FUNCTION OF n VARIABLES BY MARSTON MORSE

Ricci flow on locally homogeneous closed 4-manifolds

We discuss the Ricci flow on homogeneous 4-manifolds. After classifying these manifolds, we note that there are families of initial metrics such that we can diagonalize them and the Ricci flow preserves the diagonalization. We analyze the long time behavior of these families. We find that if a solution exists for all time, then the flow exhibits a type III singularity in the sense of Hamilton.

The Space of Symplectic Structures on Closed 4-manifolds

Let X be a 2n−dimensional smooth manifold. A 2−form ω on X is said to be non-degenerate if, for each q ∈ X and for each nonzero vector v in the tangent space TqX, there is a tangent vector v ∈ TqX such that ω(u, v) 6= 0. A symplectic structure onX is a non-degenerate closed 2−form. The fundamental example of a symplectic structure is ω0 = ∑ i dxi ∧ dyi on R = {(x1, y1, ..., xn, yn)}. In fact, b...