Fake spherical spaceforms of constant positive scalar curvature

Kwasik, Sławomir; Schultz, Reinhard

doi:10.1007/bf02566407

Cited by 8 publications

(4 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This affirmatively answers the question on page 11 of [9], where the authors determined under which conditions a topological spherical space form admits a metric with positive scalar curvature. Their main theorem is given as follows:…”

Section: Introduction and Main Resultssupporting

confidence: 72%

Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

Reiser¹

2020

Can. Math. Bull.

View full text Add to dashboard Cite

show abstract

Section: Introduction and Main Resultssupporting

confidence: 72%

Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

Reiser¹

2020

Can. Math. Bull.

View full text Add to dashboard Cite

show abstract

“…The phenomena described in Theorem 1.7 was previously known to exist, and the result provides infinite sets of simply connected and nonsimply connected examples that answer in the negative the propagation question of Kwasik-Schultz [33] that was mentioned before. LeBrun displayed a smooth structure on a 4-manifold with fundamental group Z/2 that has negative Yamabe invariant, while its universal cover has positive Yamabe invariant [35,Theorem 1].…”

Section: Theorem 17 the Orbit Spaces Of The Infinite Set Of Exotic Gmentioning

confidence: 81%

On entropies, $${\mathcal {F}}$$ F -structures, and scalar curvature of certain involutions

Torres

2015

Geom Dedicata

View full text Add to dashboard Cite

In this short note, we analyze geometric properties of orbit spaces of certain involutions in dimensions four, five, and six. We consider constructions of F -structures on manifolds of dimension at least four that allows us to study minimal entropy, minimal volume, collapse with bounded curvature, and sign of the Yamabe invariant, and its vanishing, building on work of Paternain-Petean. The existence of Riemannian metrics of vanishing topological entropy on the orbit spaces is investigated as well.

show abstract

“…2. If X 10 is orientable but not Spin, then X 10 admits a metric of positive scalar curvature if and only if A( X 10 ) = 0, where X 10 is the universal cover of X 10 [34] [106].…”

Section: Cusp Fibered D-metric Gmentioning

confidence: 99%

GEOMETRY OF SPIN ANDSPIN^cSTRUCTURES IN THE M-THEORY PARTITION FUNCTION

Sati

2012

Rev. Math. Phys.

View full text Add to dashboard Cite

We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta invariants upon variation of the Spin structure. The main sources of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spinccase and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in 10 dimensions, the (mod 2) index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the α-invariant, which in general depends on the Spin structure. This reveals many interesting connections to positive scalar curvature manifolds and constructions related to the Gromov–Lawson–Rosenberg conjecture. In the 12-dimensional theory bounding M-theory, we study similar geometric questions, including choices of metrics and obtaining elements of K-theory in 10 dimensions by pushforward in K-theory on the disk fiber. We interpret the latter in terms of the families index theorem for Dirac operators on the M-theory circle and disk. This involves superconnections, eta forms, and infinite-dimensional bundles, and gives elements in Deligne cohomology in lower dimensions. We illustrate our discussion with many examples throughout.

show abstract

Fake spherical spaceforms of constant positive scalar curvature

Cited by 8 publications

References 56 publications

Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

On entropies, $${\mathcal {F}}$$ F -structures, and scalar curvature of certain involutions

GEOMETRY OF SPIN ANDSPIN^cSTRUCTURES IN THE M-THEORY PARTITION FUNCTION

Contact Info

Product

Resources

About

Fake spherical spaceforms of constant positive scalar curvature

Cited by 8 publications

References 56 publications

Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

On entropies, $${\mathcal {F}}$$ F -structures, and scalar curvature of certain involutions

GEOMETRY OF SPIN ANDSPINcSTRUCTURES IN THE M-THEORY PARTITION FUNCTION

Contact Info

Product

Resources

About

GEOMETRY OF SPIN ANDSPIN^cSTRUCTURES IN THE M-THEORY PARTITION FUNCTION