By Igusa K.

**Read or Download Axioms for higher torsion invariants of smooth bundles PDF**

**Similar geometry and topology books**

**L²-invariants: theory and applications to geometry and K-theory**

In algebraic topology a few classical invariants - reminiscent of Betti numbers and Reidemeister torsion - are outlined for compact areas and finite team activities. they are often generalized utilizing von Neumann algebras and their strains, and utilized additionally to non-compact areas and endless teams. those new L2-invariants include very fascinating and novel details and will be utilized to difficulties bobbing up in topology, K-Theory, differential geometry, non-commutative geometry and spectral concept.

Ebook by means of Rham, G. de, Maumary, S. , Kervaire, M. A.

- The theory of the imaginary in geometry
- Discovering Geometry: An Investigative Approach
- Ebene Geometrie: axiomatische Begründung der euklidischen und nichteuklidischen Geometrie
- Geometry and quantum physics

**Additional resources for Axioms for higher torsion invariants of smooth bundles**

**Example text**

121 The Darboux process and a noncommutative bispectral problem: some explorations and challenges F. Alberto Gr¨unbaum . . . . . . . . . . . . . . . . . . . . . . . . 161 Conjugation spaces and edges of compatible torus actions Jean-Claude Hausmann and Tara Holm . . . . . . . . . . . . . . . . 179 Nonabelian localization for U(1) Chern–Simons theory Lisa Jeffrey and Brendan McLellan .

If f ∈ t, then f X is a Killing vector field. Now we fix a K ∈ t. Let · (X ) be the vector space of smooth forms on X . Let L K X denote the associated Lie derivative operator acting on the de Rham complex ( · (X ), d X ). The Cartan formula asserts that L K X = [d X , i K X ]. 1), i K X denotes interior multiplication by K X . 1) is actually an anticommutator. Duistermaat–Heckman formulas and index theory 5 Put d KX = d X + i K X . 1) can be rewritten in the form d KX,2 = L K X . , of the forms α which are such that L K X α = 0.

We can identify N X K / X to the normal bundle N M K /M . By a construction given in [B86a], (T H M, g T X ) determine a unique Euclidean connection on T X . This connection restricts to the Levi-Civita connection along the fibre X . If g T M is a metric on M such that g T M restricts to g T X on T X , and moreover T H M and T X are orthogonal in T M with respect to g T M , then ∇ T X is the projection of the Levi-Civita connection ∇ T M on T M with respect to the splitting T M = T H M ⊕ T X . Of course ∇ T X is T -invariant.