We consider homotopy classes of non-singular vector fields on three-manifolds with boundary and we define for these classes torsion invariants of Reidemeister type. We show that torsion is well-defined and equivariant under the action of the appropriate homology group using an elementary and self-contained technique. Namely, we use the theory of branched standard spines to express the difference between two homotopy classes as a combination of well-understood elementary catastrophes. As a special case we are able to reproduce Turaev's theory of Reidemeister torsion for Euler structures in the special case of closed manifolds of dimension three

Amendola, G., Benedetti, R., Costantino, F., Petronio, C. (2001). Branched Spines of 3-Manifolds and Reidemeister Torsion of Euler Structures. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, 32(1), 1-33.

Branched Spines of 3-Manifolds and Reidemeister Torsion of Euler Structures

AMENDOLA, GENNARO;
2001

Abstract

We consider homotopy classes of non-singular vector fields on three-manifolds with boundary and we define for these classes torsion invariants of Reidemeister type. We show that torsion is well-defined and equivariant under the action of the appropriate homology group using an elementary and self-contained technique. Namely, we use the theory of branched standard spines to express the difference between two homotopy classes as a combination of well-understood elementary catastrophes. As a special case we are able to reproduce Turaev's theory of Reidemeister torsion for Euler structures in the special case of closed manifolds of dimension three
Articolo in rivista - Articolo scientifico
Scientifica
3-manifold, branched spine, Reidemeister torsion, Euler structure
English
Amendola, G., Benedetti, R., Costantino, F., Petronio, C. (2001). Branched Spines of 3-Manifolds and Reidemeister Torsion of Euler Structures. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, 32(1), 1-33.
Amendola, G; Benedetti, R; Costantino, F; Petronio, C
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/8641
Citazioni
  • Scopus 3
  • ???jsp.display-item.citation.isi??? ND
Social impact