Hodge theory on Alexander invariants – a survey

AbstractWe present a cohomological proof that recurrence of suitable Teichmüller geodesics implies unique ergodicity of their terminal foliations. This approach also yields concrete estimates for periodic foliations and new results for polygonal billiards.

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Hodge theory for elliptic complexes over unital $$C^*$$ C ∗ -algebras

Annals of Global Analysis and Geometry ◽

10.1007/s10455-013-9394-9 ◽

2013 ◽

Vol 45 (3) ◽

pp. 197-210 ◽

Cited By ~ 2

Author(s):

Svatopluk Krýsl

Keyword(s):

Hodge Theory ◽

C Algebras ◽

Elliptic Complexes

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Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta

International Journal of Modern Physics A ◽

10.1142/s0217751x15501158 ◽

2015 ◽

Vol 30 (20) ◽

pp. 1550115 ◽

Cited By ~ 4

Author(s):

D. Shukla ◽

T. Bhanja ◽

R. P. Malik

Keyword(s):

Present Method ◽

Hodge Theory ◽

Rigid Rotor ◽

Normal Ordering ◽

Creation And Annihilation Operators ◽

Basic Concepts ◽

Definition Of ◽

Continuous Symmetries ◽

Internal Symmetries ◽

Theory Lead

We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one [Formula: see text]-dimensional (1D) rigid rotor without using the definition of the canonical conjugate momenta anywhere. Our present method of derivation of the basic brackets is conjectured to be true for a class of theories that provide a set of tractable physical examples for the Hodge theory.

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Almost direct summands

Nagoya Mathematical Journal ◽

10.1017/s0027763000010898 ◽

2014 ◽

Vol 214 ◽

pp. 195-204 ◽

Cited By ~ 1

Author(s):

Bhargav Bhatt

Keyword(s):

Direct Summand ◽

Hodge Theory ◽

Fundamental Theorems ◽

Ramification Locus

AbstractWe prove new cases of the direct summand conjecture using fundamental theorems inp-adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies entirely in characteristicp.

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