Graph manifolds have virtually positive Seifert volume

نویسندگان

  • Pierre Derbez
  • Shicheng Wang
چکیده

This paper shows that the Seifert volume of each closed non-trivial graph manifold is virtually positive. As a consequence, for each closed orientable prime 3-manifold N , the set of mapping degrees D(M,N) is finite for any 3-manifold M , unless N is finitely covered by either a torus bundle, or a trivial circle bundle, or the 3-sphere.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ar X iv : 1 60 3 . 03 55 8 v 1 [ m at h . G T ] 1 1 M ar 2 01 6 CONTROLLED VIRTUAL VOLUME REPRESENTATIONS AND EFFICIENT VIRTUAL DOMINATIONS

We show that for any close orientable 3–manifold with non-vanish simplicial volume, the growth of the Seifert volume (representation volume to IsoeS̃L2(R)) of its finite covers is faster than the linear rate. In particular each closed oriented 3-manifold with positive simplicial volume has virtually positive Seifert volume, which strengthens the significance of the Seifert volume. The proof is b...

متن کامل

S ep 2 00 2 HEEGAARD SPLITTINGS , THE VIRTUALLY HAKEN CONJECTURE AND PROPERTY ( τ )

The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have many ramifications for 3-manifold theory. In this paper, we ...

متن کامل

Heegaard Splittings, the Virtually Haken Conjecture and Property (τ )

The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have many ramifications for 3-manifold theory. In this paper, we ...

متن کامل

Heegaard Gradient of Seifert 3-manifold

The infimal Heegaard gradient of a compact 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3-manifolds, and show that a Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it it virtually fibers over the circle or over a surface other than the 2-sphe...

متن کامل

Heegaard Gradient of Seifert Fibered 3-manifolds

The infimal Heegaard gradient of a 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3manifolds, and show that a compact orientable Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it virtually fibers over the circle or over a surface other than the...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. London Math. Society

دوره 86  شماره 

صفحات  -

تاریخ انتشار 2012