Transfers for ramified covering maps in homology and cohomology
نویسندگان
چکیده
Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the homology transfer. This duality allows us to show that our homology transfer coincides with the one given by L. Smith. With our definition of the homology transfer we can give simpler proofs of the properties of the known transfer and of some new ones. Our transfers can also be defined in Karoubi’s approach to homology and cohomology. Furthermore, we show that one can define mixed transfers from other homology or cohomology theories to the ordinary ones.
منابع مشابه
Homological methods in algebraic map theory
The primary intent of the present paper is to adapt familiar notions of algebraic topology, such as the fundamental group, homology, and cohomology to the context of algebraic maps and their (ramified) covering projections. The notion of a principal derived map is already fairly well understood in terms of the defining voltages; however, once it is recognized that voltages are essentially cohom...
متن کاملSimplicial ramified covering maps
In this paper we define the concept of a ramified covering map in the category of simplicial sets and we show that it has properties analogous to those of the topological ramified covering maps. We show that the geometric realization of a simplicial ramified covering map is a topological ramified covering map, and we also consider the relation with ramified covering maps in the category of simp...
متن کاملBOUNDED COHOMOLOGY AND l1-HOMOLOGY OF THREE-MANIFOLDS
In this paper we define, for each aspherical orientable 3-manifold M endowed with a torus splitting T , a 2-dimensional fundamental l1-class [M ] whose l1norm has similar properties as the Gromov simplicial volume of M (additivity under torus splittings and isometry under finite covering maps). Next, we use the Gromov simplicial volume of M and the l1-norm of [M ] to give a complete characteriz...
متن کاملCounting Ramified Coverings and Intersection Theory on Spaces of Rational Functions I (cohomology of Hurwitz Spaces)
The Hurwitz space is a compactification of the space of rational functions of a given degree. The Lyashko–Looijenga map assigns to a rational function the set of its critical values. It is known that the number of ramified coverings of CP by CP with prescribed ramification points and ramification types is related to the degree of the Lyashko–Looijenga map on various strata of the Hurwitz space....
متن کاملOn continuous cohomology of locally compact Abelian groups and bilinear maps
Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2006 شماره
صفحات -
تاریخ انتشار 2006