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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

2 votes
0 answers
93 views

A roof genus of high dimensional lens space

Let $p$ be a natural number, and for $i\in \{0, ..., p-1\}$, denote the irreducible rank one complex representation of $\mathbb{Z}/p$. by $\rho_{i}$. Let $a=(a_{1},\ldots a_{d}) $ b …
7 votes
1 answer
220 views

Five-dimensional manifolds fibering over a fixed hyperbolic surface

I am aware of the classical work by Smale and Barden computing the diffeomorphism type of smooth simply connected 5-manifolds in D. Barden, Simply connected five-manifolds, Ann. of Math. (2) 82 (1965) …
9 votes
1 answer
425 views

Atiyah Bott-Shapiro orientation Vs Anderson-Brown-Peterson Splitting

Are the Atiyah-Bott-Shapiro Orientation and the Anderson-Brown-Peterson Splitting compatible in any sense? The first guess is that the ABS-Orientation is related to the projections o …
3 votes
2 answers
813 views

Reference for de Rham cohomology for physicists

Do you know a basic reference to introduce an undergraduate student with more physical rather than mathematical background to De Rham cohomology? The Student (from a Bachelors …
8 votes
1 answer
366 views

Morse Theory and proper actions

Is there some reference containing an ellaboration of Morse Theory for proper actions of Lie groups?