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- Boris I. Botvinnik, PETER B. GILKEYy
- 1995

We use the eta invariant to detect families of non bordant metrics of positive scalar curvature on spin manifolds with non trivial nite fundamental groups of odd dimension Let M be a compactâ€¦ (More)

- Kazuo Akutagawa, Boris I. Botvinnik
- 2001

We study a particular class of open manifolds. In the smooth category these are manifolds with cylindrical ends. We give a natural setting for the conformal geometry on such manifolds including anâ€¦ (More)

- Kazuo Akutagawa, Boris I. Botvinnik
- 2008

We define a relative Yamabe invariant of a smooth manifold with given conformal class on its boundary. In the case of empty boundary the invariant coincides with the classic Yamabe invariant. Weâ€¦ (More)

vanishes Note that index D M unlike the dimension of the ker nel and the dimension of the cokernel of D M is independent of the metric used in the construction of D M In fact according to the Atiyahâ€¦ (More)

- Boris I. Botvinnik, PETER B. GILKEYy
- 1996

We use the eta invariant to show every non-simply connected spherical space form of dimension m 5 has a count-able family of non bordant metrics of positive scalar curvature. Let M be a compactâ€¦ (More)

The Yamabe invariant is an invariant of a closed smooth manifold defined using conformal geometry and the scalar curvature. Recently, Petean showed that the Yamabe invariant is non-negative for allâ€¦ (More)

- Kazuo Akutagawa, Boris I. Botvinnik
- 2008

We study here compact manifolds with positive scalar curvature metrics. We use the relative Yamabe invariant from [1] to define the conformal cobordism relation on the category of such manifolds. Weâ€¦ (More)

- Kazuo Akutagawa, Boris I. Botvinnik, Osamu Kobayashi, Harish Seshadri
- 2002

For a compact manifold M of dimM = n â‰¥ 4, we study two conformal invariants of a conformal class C on M . These are the Yamabe constant YC(M) and the L n 2 norm WC(M) of the Weyl curvature. We proveâ€¦ (More)

We study the question of existence of a Riemannian metric of positive scalar curvature metric on manifolds with the Sullivanâ€“Baas singularities. The manifolds we consider are Spin and simplyâ€¦ (More)

We study a behavior of the conformal Laplacian operatorLg on a manifold with tame conical singularities: when each singularity is given as a cone over a product of the standard spheres. We study theâ€¦ (More)