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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 21st 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added very briefly a disambiguation line to the top of the entry [[genus]]. But eventually I guess we may need a genuine disambiguation page.

   I have added very briefly a disambiguation line to the top of the entry genus. But eventually I guess we may need a genuine disambiguation page.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 22nd 2012
   • (edited May 22nd 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added to _[[genus]]_ a quick comment saying that at least some important genera may be thought of as encoding [[sigma-models]]: the map $\sigma : M G \to R$ from the classifying space of $G$-structured manifolds ([[Thom spectrum]]) to some "classifying spectrum" for a class of QFTs encodes the map that sends a [[target space]] to the corresponding $\sigma$-model (e.g. [[A-hat genus]] and [[Witten genus]]). This needs to be expanded on, but I leave it at that for the moment.

   have added to genus a quick comment saying that at least some important genera may be thought of as encoding sigma-models: the map $\sigma : M G \to R$ from the classifying space of $G$-structured manifolds (Thom spectrum) to some “classifying spectrum” for a class of QFTs encodes the map that sends a target space to the corresponding $\sigma$-model (e.g. A-hat genus and Witten genus).

   This needs to be expanded on, but I leave it at that for the moment.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 13th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have expanded a bit at _[[genus]]_. Expanded the Idea-section, started some brief notes on logarithms and characteristic series, gave some of these for the examples, added more of the historical references and more reviews. But then entry would still need more work.

   I have expanded a bit at genus. Expanded the Idea-section, started some brief notes on logarithms and characteristic series, gave some of these for the examples, added more of the historical references and more reviews.

   But then entry would still need more work.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMar 22nd 2014
   • (edited Mar 22nd 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a brief paragraph on the definition of Hirzebruch series [via orientations in generalized cohomology](http://ncatlab.org/nlab/show/genus#HirzebruchSeriesViaOrientationsInGeneralizedCohomology), pointing to section 3 in Ando-Hopkins-Rezk. Wanted to do more, but am out of time for today.

   added a brief paragraph on the definition of Hirzebruch series via orientations in generalized cohomology, pointing to section 3 in Ando-Hopkins-Rezk.

   Wanted to do more, but am out of time for today.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 27th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have tried to improve [that section](http://ncatlab.org/nlab/show/genus#HirzebruchSeriesViaOrientationsInGeneralizedCohomology) a bit more (the previous wording on how the rationalization enters had been rather unclear).

   I have tried to improve that section a bit more (the previous wording on how the rationalization enters had been rather unclear).

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMar 29th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave expanded a tad at _[genus -- The Hirzebruch formula](http://ncatlab.org/nlab/show/genus#HirzebruchFormula)_ on how to read this via the splitting principle. I made related brief additions at _[[Chern class]]_, _[[Pontryagin class]]_, _[[splitting principle]]_ and maybe elsewhere.

   Have expanded a tad at genus – The Hirzebruch formula on how to read this via the splitting principle. I made related brief additions at Chern class, Pontryagin class, splitting principle and maybe elsewhere.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJun 9th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Friedrich Hirzebruch]], Thomas Berger, Rainer Jung, *Manifolds and Modular Forms*, Aspects of Mathematics **20**, Viehweg (1992), Springer (1994) &lbrack;[doi:10.1007/978-3-663-10726-2](https://doi.org/10.1007/978-3-663-10726-2)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/genus/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/genus/36">v36</a>, <a href="https://ncatlab.org/nlab/show/genus">current</a>

   added pointer to:

   • Friedrich Hirzebruch, Thomas Berger, Rainer Jung, Manifolds and Modular Forms, Aspects of Mathematics 20, Viehweg (1992), Springer (1994) [doi:10.1007/978-3-663-10726-2]

   diff, v36, current