Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with gt.geometric-topology
Search options questions only
not deleted
user 27004
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
6
votes
0
answers
84
views
Triple data for Pontrjagin dual of the Spin bordism group
It is said that the Pontrjagin dual of the 3-dimensional Spin bordism group of $BG$ for $G$ a finite group,
$$
\text{Hom}(Ω^{spin}_3(BG),\mathbb{R/Z}),
$$
can be expressed by triples of cochains $$(w …
- 10.5k
1
vote
0
answers
370
views
The relations between some 3-components links and trefoil knots [closed]
It is intuitive to see that the 3-components links (under Alexander–Briggs notations) $6^3_1, 6^3_2, 6^3_3$ are closely related to each other; in a sense by doing a cut-gluing or sew-gluing surgery, w …
- 10.5k
6
votes
1
answer
670
views
Generalized projective spaces, spheres, and exotic spheres [closed]
I like to explore and ask for proper references for the relations between generalized projective spaces, spheres, and exotic spheres:
The real projective space
$\mathbb{RP}^1 \simeq S^1,$
is homeomo …
- 10.5k
10
votes
1
answer
601
views
Non-triangulable 4-manifold as a boundary of some 5 manifold
We know that there are non-triangulable 4-manifolds, such as the E$_8$ manifold.
Can E$_8$ manifold be a boundary of some 5-manifold $M_5$? Can such a $M_5$ be triangulable or non-triangulable? What …
- 10.5k
3
votes
0
answers
171
views
Cobordant of 5d manifolds, and the generalization of bordisms
Some of the 5-dimensional manifolds are (co)bordant via oriented cobordism.
For example, if I understand correctly, 5-dimensional Dold manifold and Wu manifold are manifolds which are cobordant to …
- 10.5k
8
votes
0
answers
196
views
"Gerbes" in the cobordism theory
In a lecture I attended today, I heard the use of gerbes in the cobordism theory.
Previously, I use cobordism theory, but I never encounter the term "gerbes" when I work on bordism or cobordism group …
- 10.5k
5
votes
0
answers
160
views
Twisted spin-bordism invariant and a possible Postnikov square from $d=2$ to $d=5$
This is a follow up more advanced question following Twisted spin bordism invariants in 5 dimensions. We follow the definitions in the earlier post.
I had discussed my computation of
$$
\Omega_5^{S …
- 10.5k
4
votes
0
answers
234
views
Any cobordism invariant made of "characteristic classes", on unorientable manifolds, must be...
For any cobordism invariant (or simply bordism invariant) quantity $\omega$ that satisfy the conditions:
$\omega$ can be fully decomposed from the cup product of characteristic classes (such as Stie …
- 10.5k
5
votes
1
answer
511
views
Computation of $\Omega^{Pin-}_{d}(B\mathbb{Z}_2)$ and Smith isomorphism
question: I am looking for the literature with the result or the computation of Pin- bordism group: $\Omega^{Pin-}_{d}(B\mathbb{Z}_2)$. Can someone point out some useful ways to do this or any help …
- 10.5k
2
votes
1
answer
161
views
string bordism group and framed bordism group for $d \leq 6$ and $d \geq 7$
Why do the string bordism group and the framed bordism group
coincide the same in dimensions lower than 7 ($d = 0,1,2,3,4,5, 6$)?
Why do the string bordism group and the framed bordism group differ
…
- 10.5k
1
vote
0
answers
121
views
Determine all possible magnetic monopole of gauge theories
In Wikipedia, it states about the magnetic monopole of the gauge theory is determined by the fact:
This argument for monopoles is a restatement of the lasso argument for a pure U(1) theory. It gen …
- 10.5k
3
votes
0
answers
880
views
Quotient space, homogeneous space, and higher homotopy groups
Preparation and my input:
For the quotient space $G/H$, knowing the homotopy
groups of $G$ and $H$ one can determine homotopy groups from the long
exact sequence
$$
...
\to \pi_n(H) \to \pi_n(G) …
- 10.5k
4
votes
0
answers
239
views
Non-spin 5-manifold and $2^2$-Bockstein homomorphism
The $2^2$-Bockstein is $\beta_4$ is associated to
$$0\to\mathbb{Z}/2\to\mathbb{Z}/{8}\to\mathbb{Z}/{4}\to 0,$$
(The $2^n$-Bockstein homomorphism
$$\beta_{2^n}:H^*(-,\mathbb{Z}/{2^n})\to H^{*+1}(-,\m …
- 10.5k
3
votes
1
answer
259
views
Poincaré dual of the generators of $H^d(\mathbb{RP}^5,\mathbb{Z}_2)$
We know $H^d(\mathbb{RP}^5,\mathbb{Z}_2)=\mathbb{Z}_2$. So there are two classes of $\mathbb{Z}_2$ generators, trivial and nontrivial, for $d=0,1,2,3,4,5$.
Wha are the Poincaré dual $(5-d)$-dimension …
- 10.5k
6
votes
0
answers
624
views
Quotient space, a fundamental group, and higher homotopy groups 2
Previously, I ask for comments/suggestions on setting up the calculation in Quotient space, homogeneous space, and higher homotopy groups. There, however, I was looking for whatever methods and tools …
- 10.5k