arXiv subjects

Carlos Moraga Ferrandiz

Publications and source records attributed to Carlos Moraga Ferrandiz.

3 recordsLinked to original sources

arXiv2018

A geometric Morse-Novikov complex with infinite series coefficients

Let M be a closed n-dimensional manifold, n > 2, whose first real cohomology group H 1 (M ; R) is non-zero. We present a general method for constructing a Morse 1-form $α$ on M , closed but non-exact, and a pseudo-gradient X such that the differential $\partial$ X of the Novikov complex of the pair ($α$, X) has at least one incidence coefficient which is an infinite series. This is an application of our previous study of the homoclinic bifurcation of pseudo-gradients of multivalued Morse functions.

math.GT↗

arXiv2014

Elimination of extremal index zeroes from generic paths of closed 1-forms

Let $α$ be a Morse closed $1$-form of a smooth $n$-dimensional manifold $M$. The zeroes of $α$ of index $0$ or $n$ are called \emph{centers}. It is known that every non-vanishing de Rham cohomology class $u$ contains a Morse representative without centers. The result of this paper is the one-parameter analogue of the last statement: every generic path $ (α_t)_{t\in [0,1]}$ of closed $1$-forms in a fixed class $u\neq 0$ such that $α_0, α_1$ have no centers, can be modified relatively to its extremities to another such path $ (β_t)_{t\in [0,1]}$ having no center at all.

math.GT↗

arXiv2014

The s-cobordism theorem seen as a particular case of Latour's theorem

We show how Latour's theorem can be understood as a natural generalization of the $ s $-cobordism theorem for cohomology classes $ u\in H^1(M;\mathbb{R}) $. The $ s $-cobordism theorem becomes a special degenerate case when $ u=0 $.

math.GT↗