Torus surgeries in dimension four (or called $C^\infty$-log transformations) have been widely employed to construct a stable generalized complex 4-manifold with nonempty type change locus. We find a torus surgery in dimension six which can be applied to a stable generalized 6-complex manifold to yield a new stable generalized complex 6-manifold. Each torus surgery has an effect of increasing the number of path-connected components on the type change locus by one as in dimension four. Using this torus surgery, we prove that there exist countably infinite stable generalized complex 6-manifolds with nonempty type change locus that are not homologically equivalent to a product of lower dimensional manifolds. Also, it is shown that any finitely presented group is the fundamental group of a stable generalized complex 6-manifold with nonempty type change locus on which each path-connected component is diffeomorphic to $T^4$.

Constructions of stable generalized complex 6-manifolds and their fundamental groups / Mun, Ui Ri. - (2018 Sep 14).

Constructions of stable generalized complex 6-manifolds and their fundamental groups

Mun, Ui Ri
2018-09-14

Abstract

Torus surgeries in dimension four (or called $C^\infty$-log transformations) have been widely employed to construct a stable generalized complex 4-manifold with nonempty type change locus. We find a torus surgery in dimension six which can be applied to a stable generalized 6-complex manifold to yield a new stable generalized complex 6-manifold. Each torus surgery has an effect of increasing the number of path-connected components on the type change locus by one as in dimension four. Using this torus surgery, we prove that there exist countably infinite stable generalized complex 6-manifolds with nonempty type change locus that are not homologically equivalent to a product of lower dimensional manifolds. Also, it is shown that any finitely presented group is the fundamental group of a stable generalized complex 6-manifold with nonempty type change locus on which each path-connected component is diffeomorphic to $T^4$.
Torres Ruiz, Rafael
Mun, Ui Ri
File in questo prodotto:
File Dimensione Formato  
thesis_Mun.pdf

accesso aperto

Tipologia: Tesi
Licenza: Non specificato
Dimensione 866.58 kB
Formato Adobe PDF
866.58 kB Adobe PDF Visualizza/Apri

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/20.500.11767/82354
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact