On Injective Homomorphisms between Teichmüller Modular Groups I

نویسندگان

  • NIKOLAI V. IVANOV
  • JOHN D. MCCARTHY
  • J. D. MCCARTHY
چکیده

In this paper and its sequel, we prove that injective homomorphisms between Teichmüller modular groups of compact orientable surfaces are necessarily isomorphisms, if an appropriately measured “size” of the surfaces in question differs by at most one. In particular, we establish the co-Hopfian property for modular groups of surfaces of positive genus.

برای دانلود رایگان 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

On Injective Homomorphisms between Teichm Uller Modular Groups

In this paper we prove that injective homomorphisms between Te-ichm uller modular groups of compact orientable surfaces are necessary isomor-phisms, if an appropriately measured \size" of the surfaces in question diiers by at most one. In particular, we establish the co-Hoppan property for modular groups of surfaces of positive genus.

متن کامل

On natural homomorphisms of local cohomology modules

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

متن کامل

Mining Tree Patterns with Partially Injective Homomorphisms

One of the main differences between ILP and graph mining is that while pattern matching in ILP is mainly defined by homomorphism (subsumption), it is the subgraph isomorphism in graph mining. Using that subgraph isomorphisms are injective homomorphisms, we bridge the gap between the two pattern matching operators with partially injective homomorphisms, which are homomorphisms requiring the inje...

متن کامل

Math 627 A : Modern Algebra I Notes on the Isomorphism Theorems for Groups 1 Fundamental Results : Up to the First Isomorphism Theorem

A brief comment about items (3) and (4). If H is a subgroup of G the inclusion map is an injective homomorphism from H to G . On the other hand, the image of an injective homomorphism α : H −→ G is a subgroup that is isomorphic to H . So the study of injective homomorphisms is (up to isomorphism) the study of subgroups. After studying subgroups, we defined normal subgroup and showed several equ...

متن کامل

Diffeomorphism groups of critical regularity

Let M be a circle or a compact interval, and let α “ k ` τ ě 1 be a real number such that k “ tαu. We write Diff`pMq for the group of orientation preserving Ck diffeomorphisms of M whose kth derivatives are Hölder continuous with exponent τ. We prove that there exists a continuum of isomorphism types of finitely generated subgroups G ď Diff`pMq with the property that G admits no injective homom...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005