Pseudocycles and Integral Homology
نویسنده
چکیده
We describe a natural isomorphism between the set of equivalence classes of pseudocycles and the integral homology groups of a smooth compact manifold. Our arguments generalize to settings well-suited for applications in enumerative algebraic geometry and for construction of the virtual fundamental class in the Gromov-Witten theory.
منابع مشابه
Pseudohomology and Homology
The notion of a pseudocycle is introduced in [13] to provide a framework for defining GromovWitten invariants and quantum cohomology. This paper studies the bordism groups of pseudocycles, called pseudohomology groups. These satisfy the Eilenberg-Steenrod axioms, and, for smooth compact manifold pairs, pseudohomology is naturally equivalent to homology. Easy examples show that this equivalence ...
متن کاملFloer Homology and Invariants of Homology Cobordism
By using surgery techniques, we compute Floer homology for certain classes of integral homology 3-spheres homology cobordant to zero. We prove that Floer homology is two-periodic for all these manifolds. Based on this fact, we introduce a new integer valued invariant of integral homology 3-spheres. Our computations suggest its homology cobordism invariance.
متن کاملThe Integral Homology of the Based Loop Space on a Flag Manifold
The homology of a special family of homogeneous spaces, flag manifolds and their based loop spaces is studied. First, the rational homology ring of the based loop space on a complete flag manifold is calculated. Second, it is shown that the integral homology of the based loop space on a flag manifold is torsion free. This results in a description of the integral homology ring.
متن کاملA characterisation of S3 among homology spheres
We prove that an integral homology 3–sphere is S3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S3 . As an application we show that an irreducible integral homology sphere which is not S3 is the cyclic branched cover of odd prime order of at most four knots in S3 . A result on the structure of finite groups of odd order acting on integral ho...
متن کاملHomology Cobordism and Classical Knot Invariants
In this paper we define and investigate Z2–homology cobordism invariants of Z2–homology 3–spheres which turn out to be related to classical invariants of knots. As an application we show that many lens spaces have infinite order in the Z2–homology cobordism group and we prove a lower bound for the slice genus of a knot on which integral surgery yields a given Z2– homology sphere. We also give s...
متن کاملذخیره 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 2008