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Saturday, July 25, 2020 | History

3 edition of **Metrics of positive scalar curvature and generalised Morse functions** found in the catalog.

Metrics of positive scalar curvature and generalised Morse functions

Mark P. Walsh

- 133 Want to read
- 21 Currently reading

Published
**2011**
by American Mathematical Society in Providence, R.I
.

Written in English

**Edition Notes**

Statement | Mark Walsh |

Series | Memoirs of the American Mathematical Society -- no. 983 |

Classifications | |
---|---|

LC Classifications | QA645 .W35 2011 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL24384289M |

ISBN 10 | 9780821853047 |

LC Control Number | 2010037798 |

OCLC/WorldCa | 664450806 |

Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part 1, Mem. Amer. Math. Soc. (), no. [ pages] 3. Cobordism Invariance of the Homotopy Type of the Space of. Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics. Author: Mark Walsh Journal: Proc. Amer. Math. Soc. (), Mark Walsh, Metrics of positive scalar curvature and generalised Morse functions, Part I, .

Let (M4,g0) be a compact 4-dimensional Riemannian manifold with positive scalar curvature Rg C2 function K deﬁned on the manifold, the prescribed scalar curvature problem consists of ﬁnding a metric g, conformally related to g0, such that the scalar curvature of (M,g) is given by the function K. Writing. Aspects of Positive Scalar Curvature and Topology I MARK G. WALSH Abstract. Whether or not a smooth manifold admits a Riemann-ian metric whose scalar curvature function is strictly positive is a problem which has been extensively studied by geometers and topologists alike. More recently, attention has shifted to another intriguing problem.

[18] , Metrics of Positive Scalar Curvature and Generalised Morse Func-tions, Part I, Memoirs of AMS, No, January (Yuguang Shi) Key Laboratory of Pure and Applied Mathematics, SchoolofMathematical Sciences,PekingUniversity,Beijing, , P.R. China E-mail address: [email protected] We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survive in the (observer) moduli space of such metrics. Along the way we construct smooth fiber bundles over.

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Metrics of positive scalar curvature and generalised Morse functions, part I About this Title. Mark Walsh, Mathematisches Institut, WWU Münster. Publication: Memoirs of the American Mathematical Society Publication Year: ; VolumeNumber ISBNs:.

Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I Michael E. Taylor: University of North Carolina, Chapel Hill, Chapel Hill, NC It is well known that isotopic metrics of positive scalar curvature are concordant.

Whether or not the converse holds is an open question, at least in dimensions greater than four. Get this from a library. Metrics of positive scalar curvature and generalised Morse functions.

[Mark P Walsh]. Get this from a library. Metrics of positive scalar curvature and generalised Morse functions. Part I. [Mark P Walsh] -- "It is well known that isotopic metrics of positive scalar curvature are concordant.

Whether or not the converse holds is an open question, at. Download Citation | Metrics of positive scalar curvature and generalised Morse functions, Part II | It is well known that isotopic metrics of positive scalar curvature are concordant.

Whether or. Destination page number Search scope Search Text Search scope Search Text. by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces.

In this paper, we extend this technique to work for families of generalised Morse functions, i.e. smooth functions with both Morse and birth-death singularities. Title: Metrics of positive scalar curvature and generalised Morse functions, part 1. Authors: Mark Walsh (Submitted on 8 Nov ) Abstract: It is well known that isotopic metrics of positive scalar curvature are concordant.

Whether or not the converse holds is an open question, at least in dimensions greater than four. We show that for a. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): It is well known that isotopic metrics of positive scalar curvature are concordant.

Whether or not the converse holds is an open question, at least in dimensions greater than four. We show that for a particular type of concordance, constructed using the surgery techniques of Gromov and Lawson, this converse holds in.

The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces.

Definition. The scalar curvature S (commonly also R, or Sc) is defined as the trace of the Ricci curvature tensor with respect to the metric: = . The trace depends on the metric since the Ricci tensor is a (0,2)-valent tensor; one must first raise an index to obtain a (1,1)-valent tensor in order to take the trace.

In terms of local coordinates one can write. metrics of positive scalar curvature and generalised morse functions, part 1 by Mark Walsh, It is well known that isotopic metrics of positive scalar curvature are concordant.

Infinite loop spaces and positive scalar curvature in the presence of a fundamental group Ebert, Johannes and Randal-Williams, Oscar, Geometry & Topology, ; Manifolds with singularities accepting a metric of positive scalar curvature Botvinnik, Boris, Geometry & Topology, ; On the moduli space of positive Ricci curvature metrics on homotopy spheres Wraith, David J, Geometry &.

Metrics of positive scalar curvature and generalised Morse functions, part 1. By Mark Walsh. Abstract. It is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four.

We show that for a particular type of concordance. For positive scalar curvature non-trivial homotopy elements can be exhibited factoring the Atiyah-Bott-Shapiro map of spectra A: M Spin → KO through the space of metrics with positive scalar.

This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces. In this paper, we extend this technique to work for families of generalised Morse functions, i.e.

smooth functions with both Morse. en: Generalized Cayley surfaces. dez,: On a certain class of conformally flat Euclidean hypersurfaces. hon: Self-dual manifolds with non-negative Ricci operator. : On the obstruction group toexistence of Riemannian metrics of positive scalar curvature.

In particular, we describe a subspace of the space of positive scalar curvature concordances, parametrised by generalised Morse functions. We call such concordances Gromov-Lawson concordances. One of the main results is that positive scalar curvature metrics which are Gromov-Lawson concordant are in fact isotopic.

of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces. In this paper, we extend this technique to work for families of generalised Morse functions, i.e.

smooth. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces. In this paper, we extend this technique to work for families of generalised Morse functions, i.e.

smooth functions with both Morse and birth-death singularities. Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I. Providence: American Mathematical Society, © Material Type: Document, Updating website, Internet resource: Document Type: Internet Resource, Computer File, Continually Updated Resource: All Authors / Contributors: Mark P Walsh; American Mathematical Society.The scalar curvature problem on Ssp n an approach via Morse theory | Malchiodi A.

| download | B–OK. Download books for free. Find books.In recent years it became fashionable to study the homotopy groups of the space of Riemannian metrics of positive scalar curvature on a given closed, connected manifold and its moduli space, see.