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A Novikov fundamental group
- Source :
- International Mathematics Research Notices, International Mathematics Research Notices, 2019, ⟨10.1093/imrn/rnz032⟩, International Mathematics Research Notices, Oxford University Press (OUP), 2019, ⟨10.1093/imrn/rnz032⟩
- Publication Year :
- 2019
- Publisher :
- HAL CCSD, 2019.
-
Abstract
- Given a $1$-cohomology class $u$ on a closed manifold $M$, we define a Novikov fundamental group associated to $u$, generalizing the usual fundamental group in the same spirit as Novikov homology generalizes Morse homology to the case of non exact $1$-forms. As an application, lower bounds for the minimal number of index $1$ and $2$ critical points of Morse closed $1$-forms are obtained, that are different in nature from those derived from the Novikov homology.<br />39 pages, 4 drawings (inkscape) Added a discussion of an Hurewicz morphism and examples
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
Fundamental group
Closed manifold
General Mathematics
57R19 (Primary) 57R70, 57R17 (Secondary)
Homology (mathematics)
Morse code
01 natural sciences
Mathematics::Algebraic Topology
law.invention
Mathematics - Geometric Topology
Morse homology
law
Mathematics::K-Theory and Homology
FOS: Mathematics
0101 mathematics
Mathematics::Symplectic Geometry
Mathematics
010102 general mathematics
Geometric Topology (math.GT)
[MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG]
Differential Geometry (math.DG)
Mathematics - Symplectic Geometry
Symplectic Geometry (math.SG)
Novikov self-consistency principle
Subjects
Details
- Language :
- English
- ISSN :
- 10737928 and 16870247
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices, International Mathematics Research Notices, 2019, ⟨10.1093/imrn/rnz032⟩, International Mathematics Research Notices, Oxford University Press (OUP), 2019, ⟨10.1093/imrn/rnz032⟩
- Accession number :
- edsair.doi.dedup.....fcede436ed1562a0d5fcd0e78e1e8718