ترغب بنشر مسار تعليمي؟ اضغط هنا

Kaehlerian three-manifold groups

113   0   0.0 ( 0 )
 نشر من قبل D. Kotschick
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English
 تأليف D. Kotschick




اسأل ChatGPT حول البحث

We prove that if the fundamental group of an arbitrary three-manifold -- not necessarily closed, nor orientable -- is a Kaehler group, then it is either finite or the fundamental group of a closed orientable surface.



قيم البحث

اقرأ أيضاً

We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3-manifolds and answer questions of Reid-Wang-Zhou and Agol-Liu.
Let S be a closed topological surface. Haupts theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be realized by integration against a complex-valued 1-form that is holomorph ic with respect to some complex structure on S. We prove a refinement of this theorem that takes into account the divisor data of the 1-form.
201 - D. Kotschick 2012
Generalizing the theorem of Green--Lazarsfeld and Gromov, we classify Kaehler groups of deficiency at least two. As a consequence we see that there are no Kaehler groups of even and strictly positive deficiency. With the same arguments we prove that Kaehler groups that are non-Abelian and are limit groups in the sense of Sela are surface groups.
142 - Nicholas G. Vlamis 2020
We prove that the mapping class group of a surface obtained from removing a Cantor set from either the 2-sphere, the plane, or the interior of the closed 2-disk has no proper countable-index subgroups. The proof is an application of the automatic con tinuity of these groups, which was established by Mann. As corollaries, we see that these groups do not contain any proper finite-index subgroups and that each of these groups have trivial abelianization.
If $Gamma<mathrm{PSL}(2,mathbb{C})$ is a lattice, we define an invariant of a representation $Gammarightarrow mathrm{PSL}(n,mathbb{C})$ using the Borel class $beta(n)in mathrm{H}^3_mathrm{c}(mathrm{PSL}(n,mathbb{C}),mathbb{R})$. We show that the inva riant is bounded and its maximal value is attained by conjugation of the composition of the lattice embedding with the irreducible complex representation $mathrm{PSL}(2,mathbb{C})rightarrow mathrm{PSL}(n,mathbb{C})$. Major ingredients of independent interest are the extension to degenerate configuration of flags of a Goncharov cocycle and its study, as well as the identification of $mathrm{H}^3_mathrm{c}(mathrm{SL}(n,mathbb{C}),mathbb{R})$ as a normed space.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا