Pseudocycles and integral homology

By A. Zinger. 2006

65 citations recorded by the source corpus.

We describe a natural isomorphism between the set of equivalence classes or pseudocycles and the integral homology groups of a smooth 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ff700cf925027571cce908682c9d0071fe6342a0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. P. Seidel
2. Otto van Koert
3. Urs Frauenfelder
4. Ben Webster
5. I. Smith
6. E. Witten
7. Mark McLean

In Geometry and Topology

1. Otto van Koert
2. Urs Frauenfelder
3. P. Seidel
4. Alexander F. Ritter
5. A. Oancea
6. Nick Sheridan
7. I. Smith
8. M. Abouzaid

In Mathematical Physics

1. Otto van Koert
2. Urs Frauenfelder
3. P. Seidel
4. Alexander F. Ritter
5. A. Oancea
6. Nick Sheridan
7. I. Smith
8. M. Abouzaid

Citations in the corpus

• Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, methodology): “which satises (9.7) @(AjE) = @AjE˘= Z(1)jE q 1 jE: By imitating the construction of (9.4) with AjEinstead of K, one gets a chain homotopy (9.8) r Z(1)jE = r Z(1)jE ’r q 1 jE: Remark 9.2. We refer to [37, 21, 51] for a general discussion of the relation between equivalence classes of pseudo-cycles an”
• The Restricted Three-Body Problem and Holomorphic Curves (2018, background): “Results of Kahn, Schwarz, and Zinger [63, 98, 109], then show how to associate a homology class to a pseudocycle.”